Exam 5: Time Value of Money 2: Analyzing Annuity Cash Flows

You wish to buy a $30,000 car. The dealer offers you a 5-year loan with a 9% APR. What are the monthly payments? What is the monthly payment if you paid interest only?

The simple form of an annualized interest rate is called the annual percentage rate (APR). The effective annual rate (EAR) is a

Present Value of Multiple Annuities A small business owner visits his bank to ask for a loan. The owner states that he can repay a loan at $2,000 per month for the next three years and then $1,000 per month for the two years after that. If the bank is charging customers 8.5 percent APR, how much would it be willing to lend the business owner?

Future Value of Multiple Annuities Assume that you contribute $200 per month to a retirement plan for 15 years. Then you are able to increase the contribution to $400 per month for another 25 years. Given a 5 percent interest rate, what is the value of your retirement plan after 40 years?

Describe how compounding affects the future value computation of an annuity.

Explain why the effective annual rate (EAR) is a more accurate measure of the interest rate paid than the annual percentage rate (APR)?

Compute the future value in year 12 of a $2,000 deposit in year 3 and another $4,000 deposit at the end of year 5 using a 10% interest rate.

Number of Annuity Payments Joey realizes that he has charged too much on his credit card and has racked up $4,000 in debt. If he can pay $200 each month and the card charges percent 20 APR (compounded monthly), how long will it take him to pay off the debt?

Payday loans are very short-term loans that charge very high interest rates. You can borrow $550 today and repay $675 in two weeks. What is the compounded annual rate implied by this 22.73% rate charged for only two weeks?

What is the present value of a $1,100 payment made every year forever when interest rates are 4.5%?

Loan Balance Hank purchased a $20,000 car two years ago using an 8 percent, 5-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?

A car company is offering a choice of deals. You can receive $600 cash back on the purchase, or a 2% APR, 4-year loan. The price of the car is $18,900 and you could obtain a 4-year loan from your credit union at 6% APR. What is the monthly payment of each deal?

Present Value What is the present value of a $500 deposit in year 1 and another $100 deposit at the end of year 4 if interest rates are 5 percent?

Your current $115,000 mortgage calls for monthly payments over 30 years at an annual rate interest rate of 7%. If you pay an additional $50 each month beginning with the first payment, how much interest expense do you save by pre-paying?

Compound Frequency Say that you own a small business, which you plan to expand. Your expansion plans include borrowing $100,000 from the bank with a five-year, amortized loan. The bank has given you three loan choices: Annual payments at 8.85 percent APR Quarterly payments at 8.75 percent APR Monthly payments at 8.65 percent APR

Number of Annuity Payments Phoebe realizes that she has charged too much on her credit card and has racked up $10,000 in debt. If she can pay $300 each month and the card charges 18 percent APR (compounded monthly), how long will it take her to pay off the debt?

Annuity Interest Rate What's the interest rate of a 4-year, annual $1,000 annuity with present value of $3,500?

Your current $155,000 mortgage calls for monthly payments over 25 years at an annual rate interest rate of 6%. If you pay an additional $50 each month beginning with the first payment, how much interest expense do you save by pre-paying?

Loan Payments You wish to buy a $15,000 car. The dealer offers you a 4-year loan with a 9 percent APR. What are the monthly payments?

Your current $95,000 mortgage calls for monthly payments over 30 years at an annual rate interest rate of 6%. If you pay an additional $50 each month beginning with the first payment, how soon do you pay off your mortgage?