Dr.Ramsey

Please assist me with my discussion post.

Subject: Annuities

Systematic risk evaluates the probability and extent of negative consequences to the larger body. For example, the government has a record of intervening in the event of a probable bank failure; the government?s larger concern is the negative impact on bank customers. Some call this a governmentbail-out.

Discuss the effect on stock market investor confidence should bank customers, individuals and businesses alike, lose access to savings and undergo a loss of future purchasing power due to a bank failure

PRINTED BY: irisgarcia3@student.kaplan.edu. Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. Chapter 4 Annuities and Loans LEARNING OBJECTIVES LO1 Find the Future Value of Streams of Payments LO2 Find the Present Value of Streams of Payments LO3 Find Solutions to Advanced TVM Problems LO4 Understand Balloon and Amortized Loans Introduction This chapter extends the ideas presented in the Introduction to Time Value of Money chapter. The main extension is that this chapter presents tools for managing streams of cash flows. The first half of the chapter shows how to discount and accumulate level streams of cash flows known as annuities. The second half of the chapter explains loans and presents an indepth analysis of amortized loans, which are a type of annuity. LO1 Future Value of Streams of Payments In the last chapter, we computed the future and present values of a single deposit or sum. Often, though, you want to know the future value of a series of equal deposits over a period of time. For example, you may make equal monthly deposits into a savings account. You could find the future value of these deposits by computing the future value of each one separately and then summing them. However, this method becomes tedious if there are many deposits. An easier way to find the future value of these deposits involves using annuities. What Is an Annuity? An annuity is a series of equal payments made at equal intervals. Despite being called annuities, annuity payments don't have to be made annually. They can be made monthly, weekly, or even daily. The critical factors are that the payments equal each other and that the interval between them is the same. An annuity in which payments are made at the end of each period is an ordinary annuity. An annuity in which payments are made at the beginning of each period is an annuity due. Ordinary annuities are more common than annuities due. In this text, the annuity may be assumed to be ordinary unless otherwise specified. 1.1 Future Value of an Ordinary Annuity Suppose you want to know the future balance in your interest bearing bank account after 3 years if you make 3 annual $100 deposits. We will assume that your bank pays interest at the rate of 10% each year. The timeline of cash flows is shown in Figure 4.1. Figure 4.1 The \"long\" approach finds the future value of each cash flow and adds them up as shown in Figure 4.2. The values shown under date 3 on the timeline are just the future value of each corresponding cash flow. Figure 4.2 The total future value is the sum of the future values of the individual payments, so we can express the future value of the ordinary annuity as FVannuity = PMT1 (1 + i)n 1 + PMT2 (1 + i)n 2 + ... + PMTn 1 (1 + i)1 + PMTn (1 + i)0 Unfortunately, the equation above isn't much help in solving annuity problems. Students of algebra will recognize that the equation above is a geometric progression for which standardized solutions have been found. After some algebra, the equation simplifies to Eq. 4.1 where PMT = the periodic payment in the annuity i = the interest rate n = the number of payments The term after the multiplication sign in Eq. 4.1 is the future value interest factor for an annuity (FVIFA). The acronym is useful because it is shorter than writing out the whole formula and we will use it interchangeably with the formula. Eq. 4.2 Example 4.1 Future Value of an Ordinary Annuity: Accumulating a Nest Egg Suppose you win the lottery. The winnings consist of 20 equal annual payments of $50,000. You decide to save all of this money for your retirement, and you deposit it into an account that earns 8% per year. What is the amount of your retirement nest egg? SOLUTION Write your answers here. In this example, find the future value of an ordinary annuity: This question asks for the future value of an ordinary annuity, so FVannuity = PMT FVIFAi,n FVannuity = 50,000 45.76196 = $2,288,098.21 A Note about Rounding A good rule of thumb is to carry enough significant digits so that you can round your solution to the nearest penny. The future value of an annuity is very sensitive to changes in the interest rate. Review the Explore It to see the relationship between the future value of the annuity and the interest rate. Payments to Accumulate a Future Balance At times you will know how much you want to accumulate. The question will be how much you need to save each period to reach the goal. We can solve for the payments by substituting the definition of the annuity factor, FVIFA, into Eq. 4.1 which yields. FVannuity = PMT FVIFAi,n We can easily rearrange terms to solve for the payments. Example 4.2 Payment to Accumulate a Future Balance You hope to retire in 35 years and you need $1,000,000 in the bank to live the life you want after retirement. You can earn 7% per year on your investments. How much must you save every year to reach your goal? SOLUTION Write your answers here. Find the payment needed to accumulate $1 million. You will have to save $7,233.96 per year to have $1 million in your retirement fund after 35 years. Write your answers here. It's Time to Do a SelfTest 1. Practice computing the future value of annuities. Answer 2. A young couple wishes to accumulate $35,000 at the end of 4 years so that they can make a down payment on a house. What should their equal endofyear deposits be to accumulate the $35,000, assuming a 6% rate of interest? Algebraic Answer Excel Answer Calculator Answer Ready to do LO1 topic homework 1? 1.2 Future Value of an Annuity Due As we noted earlier, when an annuity's payments occur at the beginning of each period, we call the cash flows an annuity due. Figure 4.3 shows two variations of the 3year bank deposit example (with annual deposits of $100). The example on the top line has endofperiod timing and is an ordinary annuity. The example on the bottom line has beginningofyear payments and is an annuity due. Figure 4.3 The equation for the FV of an annuity, (Eq. 4.1) introduced earlier, provides the FV at the point in time when the last payment is made. When we apply our equation to the annuity due in Figure 4.3 we get a FV at the end of period 2, not 3. To get the FV at the end of period 3, we need to move the balance forward one period. This is done by multiplying the accumulated total at period 2 by (1 + i). More generally, for any size of payment and number of time periods, the future value of an annuity due is equal to Eq. 4.3 We can simplify this by using the future value interest factor (Eq. 4.2) for an (ordinary) annuity: FVannuity due = PMT FVIFAi,n (1 + i) The only difference between Eq. 4.1 and Eq. 4.3 is the last term (1 + i). Because of their similarity, we won't introduce a separate annuity due interest factor. Instead, we will simply multiply the ordinary annuity factor by (1 + i). Example 4.3 FV of an Ordinary Annuity and an Annuity Due You have been offered an investment opportunity that will pay you $5,000 per year for 6 years. What is the value of this stream of cash flows at the end of year 6 if you receive payments at the end of each year and you require a return of 7%? What if you receive payments at the beginning of each year? SOLUTION In this example, Write your answers here. For the ordinary annuity timing, the solution is For the annuity due timing, the solution is Write your answers here. It's Time to Do a SelfTest 3. What is the future value (at time 5) of a fiveperiod annuity due of $2,000 if the interest rate is 5%? Algebraic Answer Excel Answer Calculator Answer 4. What is the future value of an annuity due with $400 annual deposits into an account paying 7% interest over the next 8 years? Algebraic Answer Excel Answer Calculator Answer Ready to do LO1 topic homework 2? LO2 Present Value of Streams of Payments Just as we sometimes need to find the future value of a stream of equal cash flows, we also may need to find the present value of a stream of equal cash flows. In this section, we will find the present value of an ordinary annuity, an annuity due, and a perpetuity. Note that if the cash flows are different from each other, there's no equationbased shortcut. You have to compute the present value of each cash flow separately and add them together using a calculator or a spreadsheet. 2.1 Present Value of an Ordinary Annuity Consider the following present value annuity problem. You won the lottery and the prize is $100 per year at the end of each of the next 4 years. What is the present value of the prize if the interest rate is 10%? The timeline of the cash flows is shown in the figure below. Figure 4.4 One way to find the present value of the prize annuity is to find the present value of each cash flow separately and add them together. This \"long hand\" approach is shown in Figure 4.5. 4.2.2 Figure 4.5 Following this method, the general expression for the present value of an annuity is This is another example of a geometric progression that has a standardized solution. The solution to the equation can be written as Eq. 4.4 where PMT = the periodic payment in the annuity i = the interest rate n = the number of payments The term after the multiplication sign in Eq. 4.4 is the present value interest factor for an annuity (PVIFA). The acronym is useful because it is shorter than writing out the whole formula and we will use it interchangeably with the formula. Eq. 4.5 Example 4.4 PV of Ordinary Annuity You won the lottery! The prize is $100 paid at the end of each of the next 4 years. What is the present value of the lottery annuity if the interest rate is 10%? SOLUTION Write your answers here. In this example, This question asks for the present value of an ordinary annuity, so We've just discovered that the present value of a fourperiod stream of $100 cash flows is $316.99. This is the present value of the lottery prize. You would be indifferent between the four payments of $100 or a $316.99 lump sum today. It is also illuminating to think about the present value of the annuity from the point of view of the government (which runs the lottery). If the government has $316.99 to invest today, then it has just enough money to fund each of the $100 payouts. The government treasurer could invest the $316.99 at 10% and have $348.69 1 year later. The first $100 prize is then subtracted from the balance, which is reinvested. One year later, the balance is $273.56 and an additional $100 is subtracted. This process continues as shown in Figure 4.6 until the final $100 is subtracted and the remaining balance is zero. Figure 4.6 This example provides an important clue as to when you'll want to use present value equations. Anytime you want to know how much you need today to create a future cash flow stream, find the present value of the cash flows. For example, if you plan to retire at age 65 and will need $50,000 per year for the next 30 years, you compute the PV of a 30year $50,000 annuity. (If we assume an 8% return, then you would need $562,889 in your retirement account to meet this cash requirement.) Write your answers here. It's Time to Do a SelfTest 5. Practice computing the present value of an annuity. Answer 6. You've just won the lottery and will receive equal payments of $50,000 at the end of each year for the next 20 years. Your attorney offers to pay you $500,000 today if you agree to give him the stream of payments. If you think you can invest at 10%, should you accept this offer? Algebraic Answer Excel Answer Calculator Answer 2.2 Finding the Rate of Return Let's look at the retirement question from another viewpoint. Suppose you have saved $562,889 and want to withdraw $50,000 per year for 30 years. What rate of return would you need to earn? This question can be answered using the present value annuity formula, Eq. 4.4. In this example, we know the present value, the annuity payments, and the term. The unknown is the interest rate. Since this is a problem with one equation and one unknown, we can insert the variables that we know into Eq. 4.4 and solve for i The rate, i, appears in two places, so simplifying for the rate is not going to be easy. To avoid the algebra, let's get the computer to solve for the rate using trialanderror. Excel has a tool called 'Goal Seeker' that is perfect for this job. You can also use your calculator to compute the answer. The solution value is i = 8.00%. If you start with $562,889 and invest the remaining balance each year at 8%, then you will be able to withdraw $50,000 per year for 30 years. Write your answers here. It's Time to Do a SelfTest 7. You have been making $2,000 per year contributions to your company retirement plan for 20 years. It now has a balance of $250,000. If you want to withdraw $20,000 per year for 30 years, what average compounded return must you earn? Algebraic Answer Excel Answer Calculator Answer 8. You have been making $2,000 per year contributions to your company retirement plan for 20 years. It now has a balance of $250,000. What average compounded return have you earned? Algebraic Answer Excel Answer Calculator Answer 2.3 Present Value of an Annuity Due The retirement annuity problem just presented assumes end of period payments. The first payment occurs 1 year from today. The alternative timing assumption is beginning of period payments as shown in Figure 4.7. The PV of an annuity equation (Eq. 4.4) presented in Section 2.1 provides the PV one period before the first payment is due. Just as we did for future value, we will adjust our equation to multiply by 1 + i to find the PV of an annuity due at time 0. Figure 4.7 The equation for finding the present value of an annuity due is Eq.4.6 We can simplify this by using the present value interest factor for an (ordinary) annuity: PVannuity due = PMT PVIFAi, n (1 + i) The only difference between Eq. 4.6 and Eq. 4.4 is the last term (1 + i). Because of their similarity, we won't introduce a separate annuity due interest factor. Instead, we will simply multiply the ordinary annuity factor by (1 + i). Example 4.5 Present Value of an Annuity Due You won the lottery! The prize is $100 paid at the beginning of each of the next 4 years (starting today). What is the present value of the lottery annuity if the interest rate is 10%? SOLUTION Write your answers here. In this example, This questions asks for the present value of an annuity due, so PVannuity due = PMT PVIFAi, n (1 + i) Write your answers here. It's Time to Do a SelfTest 9. You just bought a building that has net rent revenues of $150,000 per year. You will receive your first rental payment today and expect to continue receiving them for the next 20 years. What is the PV of this rental stream if you can earn 6% on your investment? Algebraic Answer Excel Answer Calculator Answer 2.4 Present Value of a Level Perpetuity Annuities are streams of equal payments that go on for a fixed number of periods. If the annuity continues forever, it's called a perpetuity. The term perpetuity comes from the word perpetual, which means continual or everlasting. The intuition behind the perpetuity is easy to understand. With annuities, the balance owing falls each year as the annual cash flow is paid out. With a perpetuity, the principal must remain constant if the cash flow is to continue forever. To derive the equation for the present value of a perpetuity, consider the following. What is the dollar amount of interest earned at the end of 1 year if the principal (PV) is $1,000 and the interest rate is 10%? The answer is $100. The equation you used to calculate this is $1,000 0.10 = $100. Dividing both sides of the equation by the interest rate yields $1,000 = $100/0.10. This is the equation for the PV of a perpetuity, Eq.4.7 The cash flows from a level perpetuity (with a $100 payment) are illustrated by the following timeline. Note that the timeline incorporates an endofperiod timing assumption: the first cash flow on the timeline is at date 1. Figure 4.8 Example 4.6 Preferred Share Valuation Using the Present Value of a Perpetuity Suppose we want to determine the present value of the dividends paid by a share of preferred stock. We know that the stock promises to pay the holder an annual $100 dividend forever, and we assume a 10% interest rate. We also assume that the first dividend will be paid in 1 year. SOLUTION Write your answers here. This question asks for the present value of a level perpetuity, so PVperpetuity = PMT/i = $100/0.10 = $1,000.00 As investors, we would be willing to pay no more than $1,000.00 for a share of this stock. Write your answers here. It's Time to Do a SelfTest 10. An endowed faculty chair is created when a benefactor makes a donation of sufficient size that earnings from the donation pay the salary and benefits of a professor forever. How much would have to be donated to endow a chair in your name if the salary and benefits were $80,000 and the afterinflation interest rate was 7%? Algebraic Answer Excel Answer Calculator Answer Ready to do LO2 topic homework 1? LO3 Help with Advanced Time Value Problems The equations presented in this chapter are not difficult to calculate and do not, of themselves, present an obstacle to solving time value of money problems. The main obstacle that students face in solving advanced time value of money problems is choosing the correct equation to apply to a given scenario. This section deals with problems that many students find difficult. 3.1 Tips for Solving Time Value of Money Problems Almost all time value of money problems are word problems, but to solve them they must be expressed in the form of an equation with one unknown. Luckily, almost every problem that we confront (in this text) involves only one unknown and one equation. In time value of money mathematics, the equation is known as an equation of value. An equation of value is an equality between cash inflows and outflows after they have all been accumulated or discounted to a common point in time. This common point in time is called the focal date. The focal date is central to solving time value of money problems. Because money is more valuable the sooner it is received, we can't equate a dollar today with a dollar next year. Either we accumulate today's dollar to next year or discount next year's dollar to today. In many examples, the focal date is arbitrary it simply acts as a common point to which we can bring all payments so that an equation of value can be obtained. 4.3.2 To determine how to solve TVM problems, and to pick which equation of value to use, follow these steps. 1. Review the information given in the problem and jot down what is known. 2. Draw a timeline. 3. Select a focal date. There are only two directions that you can move money: forward or back. If you pick a focal date at the end of the timeline, then you are moving cash forward (a future value). If you pick a focal date at the beginning of the timeline, then you are moving cash backward (discounting). 4. Determine whether the cash flows are lumpsums or annuities. If you have a single cash flow or if there are multiple cash flows of varying amounts, then you are dealing with lumpsums. If there are multiple cash flows with the same value, then you have an annuity. (If the annuity goes on forever, then you have a perpetuity.) 5. Determine the compounding frequency of the problem (e.g., annual, monthly or weekly) and decide whether the cash flows are beginningofperiod or endofperiod. Here's one last suggestion. Not every problem can be solved immediately with one of the basic equations of value presented in this chapter. If you're attempting to solve a problem and find you can't determine what to plug into the equation for each of the variables, it may be because you're using the wrong equation of value. Try another. 4.3.3 3.2 Imbedded Annuities It's not unusual that cash flows have some payments that differ, as well as some that are the same. When an annuity is mixed with other irregular payments, we have an imbedded annuity. The most common use of imbedded annuities is the financial analysis of projects. We can often estimate the first few cash flows accurately, but a reasonable simplifying assumption is that later cash flows are all the same. Problems with imbedded annuities can get complicated, so we want to take time to walk through an example slowly. To solve for the present value of mixed cash flow streams, we find the present value of the annuity, then add the present value of any other cash flows. The simplest mixed cash flow is one in which there are several periods with no cash flows before the annuity begins. This is called a deferred annuity. A timeline for a simple deferred annuity is shown in Figure 4.9. We will assume an interest rate of 10%. Figure 4.9 4.3.4 We solve this problem in two steps. First, we apply the present value method to the annuity. When we do this using Eq. 4.4, we find the value of the annuity one period before the first payment. (We label this point as PV1 on the timeline.) STEP 1: We're not finished yet because we need the value at time zero, not at time 1 (the end of the first period). To move the value of the annuity back in time one more period, we treat the solution to Step 1 as a lump sum on date 1 and find its present value: STEP 2: Let's review carefully what we've done. Step 1 discounts the value of the threeperiod annuity to the end of period 1. Step 2 discounts the present value of the annuity back to time 0. A slightly more complex example has two annuities. In the following, find the present value of each annuity separately and add them together. Example 4.7 Present Value of Two Annuities Suppose you have two 3year annuities, one beginning one period from now (with $200 payments) and another beginning four periods from now (with $100 payments). What are the present values of each of the annuities, and what is their combined PV? Assume an interest rate of 10%. SOLUTION Write your answers here. We begin by drawing a timeline. These are especially important with complicated problems like this one. The focal date of this problem is time 0. To solve this problem, find the present value of each annuity separately (at time 0) and then sum the two present values. The combined present value is $497.37 + $186.84 = $684.21. Write your answers here. It's Time to Do a SelfTest 11. Practice computing the PV of imbedded annuities. Answer Ready to do LO3 topic homework 1? LO4 Loans This section presents an overview to two types of loans: (1) balloon loan and (2) amortized loan. We start with balloon loans to establish a basic understanding of how interest is calculated for a loan. Second, we present amortized loans. Car loans and mortgages are examples of amortized loans. First, we show how to calculate the payments for an amortized loan. Then we show how to separate the loan payments into their principal and interest components and how to calculate the principal outstanding using an amortization schedule. 4.1 Balloon Loans This section deals with the simplest form of a loan: the balloon loan. A balloon loan is a loan where the principal and interest (sometimes just the principal) are paid at the end of the loan term. The endofterm payment is referred to as the balloon payment. Balloon loans are very common in business. For example, shortterm construction loans are often structured with a balloon loan during the construction phase followed by a longterm amortized loan. Here, we will only analyze balloon loans where the balloon payment includes both the principal and interest. In that case, the balloon payment is just the future value of the principal when compounded at the loan rate (i) over the loan term (n). The equation of value for balloon loans is just the basic future value equation. Balloonn = FVn = Principal0 (1 + i)n Eq. 4.8 4.4.2 Example 4.8 Balloon Loan: Solve for the Balloon Payment Your friend, Ernest Defraud, wants to borrow $1,000 for 3 years. Let's assume that you want to earn interest at 5% compounded annually. What is the balloon payment? How much interest do you earn on the loan? SOLUTION Write your answers here. Since the principal of the loan is $1,000, the amount of interest earned by the lender is Interest earned = $1,157.63 $1,000 = $157.63. Write your answers here. It's Time to Do a SelfTest 12. You are going to borrow $100,000 to fund the start of your new restaurant. The bank wants to be repaid with a balloon payment in 3 years. They will charge 10% interest. How much will your payment be? Algebraic Answer Excel Answer Calculator Answer 4.2 Amortized Loans Amortized loans are loans where interest and principal are repaid with a constant series of payments, which are paid at regular time intervals. Mortgage loans are an example. The loan obligation is literally killed (mortis is the Latin word for death) by the series of constant payments. The first subsection shows how to calculate the payments in an amortized loan and the second presents the loan amortization schedule, which helps you solve for the amount of interest paid with each payment and the principal owing after each payment. Amortized Loan Payments Let's reconsider the $1,000 loan to Ernest Defraud. Instead of a balloon loan, assume that the loan is structured as an amortized loan with three annual, endofyear payments as shown in the following timeline. Figure 4.10 What set of endofyear payments does the lender require? Here is a hint: wouldn't the lender be happy to exchange the principal for the payments if the present value of the payments is the same as the principal? The hint suggests that the focal point is time 0. Notice that the payments look like an ordinary annuity. We know how to find the present value of annuity payments (recall Eq. 4.4 and Eq. 4.5). The equation of value for an amortized loan is the equality between the principal and the present value of ordinary annuity payments. Principal = PMT PVIFAi,n Eq. 4.9 We call Eq. 4.9 the amortized loan equation. The equation involves four variables: the principal, the payments, the interest rate and the number of payments. We can use it to solve for any one variable if the other three are given. In the Ernest Defraud example, the unknown is the annuity payment (PMT). We can rearrange Eq. 4.9 to solve for payments as follows. Eq. 4.10 For the loan to Ernest, the interest rate is 5% (i = 5) and there are three payments (n = 3). So, PVIFA5%,3 = 2.723248. The amortized loan payments are PMT = $1,000/2.723248 = $367.21. Example 4.9 Amortized Loans, Interest, and the Reinvestment Rate Your friend, Ernest Defraud, wants to borrow $1,000 for 3 years. He has proposed an amortized loan with payments of $367.21. What is the future value of the payments if you can reinvest the first and second payments at 5%? How much interest do you earn from reinvestment and how much interest is included in the payments themselves? SOLUTION Write your answers here. At year 3, the future value of the payments can be calculated by finding the future value of a threeperiod ordinary annuity at a rate of 5%. The future value of the annuity is The amount of interest earned due to reinvestment is just the difference between the future value of the three payments and the sum of the three payments. The sum is what you would have at year 3 if you didn't earn any interest by reinvesting. For example, if you put the payments in your mattress! Reinvestment interest = $1,157.63 (3 $367.21) = $56 The amount of interest that is included in the three payments is the difference between the sum of the three payments and the principal of the loan. Interest in payments = (3 $367.21) $1,000 = $101.63 This example highlights two important points about amortized loans: 1. Interest on amortized loan payments comes in two forms: (1) each payment contains interest and (2) the lender receives the payments before the end of the term and so can earn interest by investing them. 2. The future value of the amortized loan payments is only equal to the balloon payment if the lender can reinvest intermediate payments at the loan rate (try it with a different rate to see). Thus, lenders only earn i% on amortized loans if they can reinvest at i%. This is called the reinvestment rate assumption. Example 4.10 Solving for Amortized Loan Payments: The Car Loan Car loans are amortized loans. Consider the Ferrari California, shown at right. The California has a V8 engine that generates 450 hp. Its top speed is 193 mph, and it can reach 60 mph in less than four seconds. The price of a Ferrari California is $190,000. Let's say that your bank will lend you the money to buy the car at a rate of 6% for a 6year term with monthly payments. What are the monthly payments on the car loan? SOLUTION Write your answers here. In this example, i = 6%, n = 6, and m = 12. The monthly interest rate is the periodic rate i/m = 0.06/12 = 0.005. The number of monthly payments is n m = 6 12 = 72. The monthly payments on the loan can be solved using a monthly variation of the amortized loan identity (Eq. 4.9). For only $3,148.85 (per month) you could reach 60 mph in under 4 seconds and drive the hottest car in your neighborhood. Write your answers here. It's Time to Do a SelfTest 13. What will the equal annual endofyear payments need to be in order to fully amortize a $25,000, 12% loan, over a 5year period? Algebraic Answer Excel Answer Calculator Answer Loan Amortization Schedule Amortized loan payments are a blend of interest and principal. However, the portion of each payment that is interest and principal changes. Each payment reduces the principal owing and so reduces the amount of interest owing in the next period. We can calculate the amount of interest and principal in each payment using a loan amortization schedule. The schedule is very useful in business because interest payments are tax deductible. Consider an amortized loan with principal of $10,000, a term of 5 years, and a rate of 10%. The annual payments are $2,637.97. At the end of the first year the interest owing is Interest owing = 0.10 $10,000 = $1,000. The payment at the end of the first year is $2,637.97, thus the principal repaid at the end of the year is the amount left over after interest is paid: Principal repaid = $2,637.97 $1,000 = $1,637.97. The repayment of principal lowers the balance owing (at the end of the first year) to Principal owing = ($10,000 $1,637.97) = $8,362.03. The full schedule of payments, interest, and principal payments is shown in Table 4.1. Table 4.1 Amortized Loan Payment Schedule A B C D E 1 Year Interest Owing at End of Year Payment Principal Repayment Principal Owing at End of Year 21 1000.00 2637.97 1637.97 8362.03 32 836.20 2637.97 1801.77 6560.26 43 656.03 2637.97 1981.94 4578.32 54 457.83 2637.97 2180.14 2398.18 65 239.82 2637.97 2398.15 0.00 Look at the row labeled \"Year 2\" of Table 4.1, which shows values for the second year of the loan. Notice how interest owing at the end of the second year is $836.20, which is simply 10% of the principal owing at the end of the first year. Look at the final row of the table. Notice how the last payment covers the last amount of interest owing and repays the remaining principal. Very tidy! If you were a business owner and wanted to know your interest expense in year 2, it would be $836.20. Write your answers here. It's Time to Do a SelfTest 14. Prepare an amortization table for a $3,000 twoperiod loan assuming a 5% interest rate and annual payments. Algebraic Answer Excel Answer Calculator Answer Ready to do LO4 topic homework 1