# Annual rates and interest rates.

- Note that interest rates are always given as annual rates. If the payments are monthly, then the annual interest rate needs to be divided by 12 in order to get the rate per month. Use monthly rates in your calculations when the payments are monthly. Similarly, if the payments are monthly, then N is the number of months (not the number of years).
- It isn’t clear in problem 5-54, but assume that monthly payments are made on the car loan.
- Problem 5-58 has a typo in part a. Create a schedule for a 30-year loan (not 3-year). Also, assume that monthly payments are made on the home loan.

Word, or PDF file showing the answer and the supporting calculations. Clearly show your work with all steps included. If you are using mathematical formulas, write the formulas with all steps to get to the answer. If you are using a financial calculator, write out all the calculator keystrokes used. If you are using Excel, submit the file with formulas and the data entered into the formula. Your work must be clearly visible

**Chapter 4 and 5 Problems and Solutions**

4-12 Present Value Compute the present value of an $850 payment made in 10 years when the discount rate is 12 percent.

PV=FV/ (1+i) N

PV=$850/ (1+0.12)10

=$850 / 3.10585

=$273.68

4-24 Comparing Cash Flows Which cash flow would you rather pay, $425 today or $500 in two years if interest rates are 10 percent? Why?

4-28 Moving Cash Flows What is the value in year 15 of a $250 cash flow made in year 3 if interest rates are 11 percent?

4-30 Solving for Rates what annual rate of return is earned on a $5,000 investment when it grows to $9,500 in five years? (LG4-7)

4-32 Solving for Time How long will it take $2,000 to reach $5,000 when it grows at 10 percent per year?

FVN = PV X (1 = i) N

$5000 = $2000 X (1 + 0.10) N

(1.10)N = 5/2 (the thousands cancel)

In (1.10) N = In 2.5

N x In 1.10 = In 2.5

N = In 2.5 / In 1.10 = 0.91629 / 0.09531 = 9.61 years

= 9 years, 7.4 months

4-34 Future Value At age 25 you invest $1,500 that earns 8 percent each year. At age 40 you invest $1,500 that earns 11 percent per year. In which case would you have more money at age 65?

4-37 Solving for Rates what annual rate of return is earned on a $4,000 investment made in year 2 when it grows to $6,500 by the end of year 7?

4-41 Moving Cash Flows You are scheduled to receive a $500 cash flow in one year, a $1,000 cash flow in two years, and pay an $800 payment in three years. If interest rates are 10 percent per year, what is the combined present value of these cash flows?

5-4 Future Value of an Annuity what is the future value of a $700 annuity payment over six years if interest rates are 10 percent?

5-8 Present Value of an Annuity what’s the present value of a $700 annuity payment over six years if interest rates are 10 percent?

5-12 Present Value of an Annuity Due If the present value of an ordinary, six-year annuity is $8,500 and interest rates are 9.5 percent, what’s the present value of the same annuity due?

5-16 Effective Annual Rate A loan is offered with monthly payments and a 13 percent APR. What’s the loan’s effective annual rate?

5-20 Future Value of Multiple Annuities Assume that you contribute $150 per month to a retirement plan for 15 years. Then you are able to increase the contribution to $350 per month for the next 25 years. Given an 8 percent interest rate, what is the value of your retirement plan after the 40 years?

5-26 Present Value You are looking to buy a car. You can afford $650 in monthly payments for five years. In addition to the loan, you can make a $750 down payment. If interest rates are 8 percent APR, what price of car can you afford?

5-28 Present Value of a Perpetuity A perpetuity pays $50 per year and interest rates are 9 percent. How much would its value change if interest rates decreased to 7.5 percent? Did the value increase or decrease?

5-34 Annuity Interest Rate What’s the interest rate of a seven-year, annual $4,000 annuity with present value of $20,000?

5-40 Loan Payments You wish to buy a $10,000 dining room set. The furniture store offers you a three-year loan with an 11 percent APR. What are the monthly payments? How would the payment differ if you paid interest only? What would the consequences of such a decision be?

5-42 Number of Annuity Payments Phoebe realizes that she has charged too much on her credit card and has racked up $6,000 in debt. If she can pay $200 each month and the card charges 18 percent APR (compounded monthly), how long will it take her to pay off the debt?

5-54 Loan Balance Hank purchased a $20,000 car two years ago using a 9 percent, five-year loan. He has decided that he would sell the car now, if he could get a price that would pay off the balance of his loan. What’s the minimum price Hank would need to receive for his car?

5-58 Spreadsheet Problem When paying off a home mortgage, extra principle payments can have a dramatic impact on the time needed to pay off the mortgage. (LG5-9) a. Create an amortization schedule for a $200,000, thirty year mortgage, with a 6% APR. B. After the fifth