I need help understanding how these answers were calculated. It lists the numbers you need to plug in below, but in detail help me understand how these were calculated. I would prefer not on the finance calculator, just manually so I can understand it.

Lesson 06 Practice Problems

The followingpractice problems are very similar tothe problems you will encounter in the lesson quiz. Take the time to try to solve these sample problems; study the Detailed Explanation if you're struggling to find the solution.

Problem 1

Suppose you signed a contract for a special assignment over the next eight years. You will be paid $15,435.00 at the end of each year. If your required rate of return is 12%, what is this contract worth in today? (Show your answer to the nearest cent.)

$76,675.52

N = 8; PMT = 15435; I/Y = 12; FV = 0; CPT PV.

Problem 2

You need a loan to purchase new equipment. The loan will be paid off over 12 years with payments made at the end of every quarter. If the stated annual rate is 12% and quarterly payments are $325.00, what is the loan amount? (Show your answer to the nearest cent.)

$8,211.68

N = 12(4); I/Y = 12/4; PMT = 325; FV = 0; CPT PV.

Problem 3

You would like to purchase a car for $23426. If the car loan is 12.7% financed over five years, what will the monthly payments be for this car? (Show your answer to the nearest cent.)

$529.42

PV = 23426; I/Y = 12.7/12; N = 5(12); FV = 0; CPT PMT.

Problem 4

What is the most that you would pay for an investment that promises to pay $16,691.00 a year forever with the first payment starting one year from now? Assume that your required rate of return for this investment is 9.1%. (Show your answer to the nearest cent.)

$183,417.58

16,691 / 0.091 = 18,3417.58.

Problem 5

A loan has a stated annual rate of 9.9%. If loan payments are made monthly and interest is compounded monthly, what is the effective annual rate of interest? (Show your answer to the fourth decimal place.)

0.1036

(1 + 0.099/12)^12 - 1 = 1.10362 - 1 = 0.10362.

Problem 6

You invest $4,792.00 at the beginning of every year and your friend invests $4,792.00 at the end of every year. If you both earn an annual rate of return of 2.9%, how much will each of you have in your account after 39 years? (Show your answer to the nearest cent.)

Amount in friend's account = $338,628.53;

Amount in your accout = $348,448.76

PM = 4,792; I/Y = 2.9; N = 39; PV = 0; CPT FV = 33,8628.53 for friend.

Switch to BGN mode. 2nd PMT, 2nd Enter, 2nd CPT, then CPT PMT = 34,8448.76 Switch back to End mode

Problem 7

You currently have $3,175.00 in a retirement savings account that earns an annual return of 11%. You want to retire in 42 years with $1,000,000. How much more do you need to save at the end of every year to reach your retirement goal?

$1,037.20

PV = -3175; I/Y = 11; N = 42; FV = 100,0000; CPT PMT.

Problem 8

You currently owe $3,899.00 of your credit card that charges an annual interest rate of 16.7%. You make $111.00 of new charges every month and make a payment of $250.00 every month. What will your credit card balance be in three months?

$3,641.23

PV = 3,899; I/Y = 16.7/12; PMT = -250 + 111 = -139; N = 3; CPT FV.

Problem 9

You would like to retire in 20 years. The expected rate of inflation is 3% per year. You currently have a standard of living that requires $8,660.00 of monthly expenses. Assuming you want to maintain the same standard of living in retirement, what are your monthly expenses expected to be the first year of retirement? (Show your answer to the nearest cent.)

$15,640.92

N = 20; I/Y = 3; PV = -8660; PMT = 0; CPT FV.

Problem 10

You purchasea house for $103,426.00. You made a down payment of $20,000.00 and the remainder of the purchase price was financed with a mortgage loan. The mortgage loan is a 30-year mortgage with an annual interest rate of 4.1%. Mortgage payments are made monthly. What is the monthly amount of your mortgage payment? (Show your answer to the nearest cent.)

$403.11

PV = 103,426 - 20,000 = 83,426; N = 30(12); I/Y = 4.1/12; FV = 0; CPT PMT.

Problem 11

Prepare the first row of a loan amortization schedule based on the following information. The loan amount is for $41,161.00 with an annual interest rate of 2%. The loan will be repaid over seven years with monthly payments.

Loan payment: $525.52

Interest portion: $68.60

Principle portion: $456.92

Loan balance after first monthly payment: $40,704.08

PV = 411,61; N = 7(12); FV = 0; I/Y = 2/12; CPT PMT = 525.52

Interest portion = .02(41161)/12 = 68.60

Principle = 525.52 - 68.60 = 456.92

Loan Balance = 41,161 - 456.92 = 40,704.08.

Problem 12

What is the most you would be willing to pay for a investment that will pay you $309.00 in one year, $456.00 in two years, and $223.00 in three years, if your required rate of return for this type of investment is 20.1%?

$702.15

FV = 309; N = 1; PMT = 0; I/Y = 20.1; CPT PV = 257.286

FV = 456; N = 2; PMT = 0; I/Y = 20.1; CPT PV = 316.140

FV = 223; N = 3; PMT = 0; I/Y = 20.1; CPT PV = 128.729

257.286 + 316.140 + 128.729 = 702.15.