Exam 6: The Time Value of Money-Annuities and Other Topics

To find the present value of an annuity due, one could

What is the present value of an annuity of $12 received at the end of each year for seven years? Assume a discount rate of 11%. The first payment will be received one year from today (round to the nearest $1).

An investment will pay $500 in three years, $700 in five years, and $1,000 in nine years. If the opportunity rate is 6%, what is the present value of this investment?

You have borrowed $70,000 to buy rental property. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate the principal paid to the bank in month two of the loan. Assume end-of-period payments.

The future value of a complex cash flow growing at the rate of i for periods is its present value multiplied by (1+i)n.

You wish to borrow $12,000 to be repaid in 60 monthly installments of $257.93. The annual interest rate is

Edward Johnson decided to open up a Roth IRA. He will invest $1,800 per year for the next 35 years. Deposits to the Roth IRA will be made via a $150 payroll deduction at the end of each month. Assume that Edward will earn 8.75% annual interest compounded monthly over the life of the IRA. How much will he have at the end of 35 years?

Ronald Slump purchased a real estate investment with the following end-of-year cash flows: Year EOY Cash Flow 1 $200 2 $-350 3 $-430 4 $950 What is the present value of these cash flows if the appropriate discount rate is 20%?

Recently you borrowed money for a new car. The loan amount is $15,000 to be paid back in equal annual payments which begin today, and will continue to be payable at the beginning of each year for a total of five years. Interest on the loan is 8%. What is the amount of the loan payment?

Francis Peabody just won the $89,000,000 California State Lottery. The lottery offers the winner a choice of receiving the winnings in a lump sum or in 26 equal annual installments to be made at the beginning of each year. Assume that funds would be invested at 7.65%. Francis is trying to decide whether to take the lump sum or the annual installments. What is the amount of the lump sum that would be exactly equal to the present value of the annual installments? Round off to the nearest $1.

Suppose that you wish to save for your child's college education by opening up an educational IRA. You plan to deposit $100 per month into the IRA for the next 18 years. Assume that you will be able to earn 10%, compounded monthly, on your investment. How much will you have accumulated at the end of 18 years?

If you invest $750 every six months at 8% compounded semi-annually, how much would you accumulate at the end of 10 years?

You want to travel to Europe to visit relatives when you graduate from college three years from now. The trip is expected to cost a total of $10,000. Your parents have deposited $5,000 for you in a CD paying 6% interest annually, maturing three years from now. Aunt Hilda has agreed to finance the balance. If you are going to put Aunt Hilda's gift in an investment earning 10% annually over the next three years, how much must she deposit now so you can visit your relatives in three years?

You have just purchased a share of preferred stock for $50.00. The preferred stock pays an annual dividend of $5.50 per share forever. What is the rate of return on your investment?

To evaluate and compare investment proposals, we must adjust all cash flows to a common date.

What is the present value of an investment that pays $10,000 every year at year-end for the next five years and $15,000 every year at year-end for years six through 10? The annual rate of interest for the investment is 9%.

All else constant, an individual would be indifferent between receiving $2,000 today or receiving a $200 perpetuity when the discount rate is 10% annually.

What is the present value of an annuity of $100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest $10). The discount rate is 13%. To solve this problem with a financial calculator, the correct choice is

If you have $20,000 in an account earning 8% annually, what constant amount could you withdraw each year and have nothing remaining at the end of five years?

Your investment goal is to have $3,000,000 in 40 years for retirement. You decide to invest in a mutual fund today that pays 12% per year compounded monthly. How much must you invest at the end of each month to meet your investment goal? Round to the nearest $1.