1. Saving for a Corvette My really cool aunt says that she will sell me her 1959 perfectly restored Corvette for $15,000 when I graduate from college in 7 years (on time, with good grades) because she will be really old then and she thinks Ill take good care of it. This is an incredibly good deal so I dont want to mess it up, and I dont want to take any risks with the money. Ive decided to put the money aside now in a risk-free account earning 5%, compounded annually, and not touch it the whole time. How much do I need to put aside today? 2. Cash vs. Installment Plan Suppose that a car dealer gives you a choice between paying $15,500 for a new car or entering into an installment plan where you pay $8,000 down today and make payments of $4,000 in each of the next two years. Assuming the interest rate you can earn by depositing your money risk-free is 8%, which is the better deal? 3. Present Value of an Annuity Consider the following scenarios for an annuity with a $1000 payment amount C: a. If you invest the $1,000 at the end of each year for five years and receive a return of 7%, how much is the annuity worth in today's dollars? b. Now consider what happens if we increase the number of years of the annuity, from 5 to 6 years: i. Before calculating, predict whether the present value of the annuity will rise or fall by more or less than $1000? Describe in a few sentences why this is the case. ii. Calculate how much is the annuity worth in todays dollars to confirm your prediction. c. Now (going back to the original case in a) consider what happens if we increase the rate of return, from 7% to 8%: iii. Before calculating, predict if the present value of the annuity will rise or fall from your answer in a? Describe in a few sentences why this is the case. iv. Calculate how much is the annuity worth in todays dollars to confirm your prediction. 4. Simple vs. Compound Interest accumulation Sergio deposited $100 in each of 2 accounts. He made no deposits or withdrawals for the next 20 years. Account A earned 10% simple interest. Account B earned 10% interest, compounded annually. Complete the tables below showing the balance in each account at the end of each year, then draw 2 graphs to show the same information. Table 1 Years 0 through 10 Year 0 1 2 3 4 5 6 7 8 9 10 Balance, Account A 100 Balance, Account B 100 Table 2 Years 11 through 20 Year 11 12 13 14 15 16 17 18 19 20 Balance, Account A Balance, Account B 5. Future Value of an Annuity You just turned 12 and you want $40,000 for college at the end of your 17th year. If you are to deposit the same amount at the end of each year of your age into a risk-free account with a 5% annual interest rate, compounded annually, how much should you invest each year? 6. Amortized loans You are faced with a choice of mortgage terms to purchase a new home costing $300,000. You are able to put a $40,000 down payment on the home. The bank offers you a fixed-rate of 4.5% for a 30-year loan, and one at 4% for a 15-year loan. You have determined that you can afford up to, but not more than, a $1750 monthly mortgage payment. How do the payment amounts on the 2 loans compare? Can you afford the 15-year loan? 7. FV and PV of an Annuity Suppose you expect to live for 20 years after retiring at age 65. You would like to save enough money to have $30,000 per year to live on during your retirement. Currently, at age 30, you would like to start saving a fixed amount each year to fund this retirement plan. How much do you need to save each year to reach your goal? (Assume all annuity payments are end-of-period, ordinary annuity payments, and use a 7% interest rate, compounded annually, in your calculations). 8. The Power of Compounding Lets take the example of Doris Rude, a taxi driver in Manhattan who got into a borrowing trap with a payday-lender when she got behind on her medical bills . For a fee of $30, the payday lender agreed to advance Doris a 2-week loan of $100. Doris wrote a check for $130 that the lender agreed to hold for 2 weeks. At the end of two weeks, however, with no change in her income or living expenses, Doris could not pay back the loan and the check bounced. She went to another lender to cover the debt of the first. Soon, she was bouncing from one payday lender to the other, six in all. Though cases like Doriss have since generated increased scrutiny and regulation of the payday-loan industry, these usurious lenders still flourish and take advantage of borrowers who do not understand the power of compounding. a. What was the 2-week interest rate on the initial loan? b. Assuming Doris could not pay back any of the money that she borrowed (principal and fees/interest), and the lender continued to charge the same rate, how much money would Doris owe: i. After 6 months? ii. After 1 year? Problems 9-11 use the following information: You qualify for a home loan of $350,000 at 7% interest with a 30-year term. Payments on the loan are made monthly. You have savings of $42,000 and would like to pay this amount as a down payment. 9. Considering all your sources of borrowing and cash, what is the most expensive home you could purchase? 10. Assuming you make the $42,000 down payment and take the loan of $350,000, what is the initial loan-to-value ratio on this home loan? 11. Assume there is a financial meltdown and the value of the home falls by 15% in the first year. After 12 months, your loan balance is $346,445. What is the loan-to-value ratio after one year