Exam 4: Time Value of Money

Your girlfriend just won the Florida lottery. She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. What rate of return is built into the annuity?

Suppose a State of New York bond will pay $1,000 ten years from now. If the going interest rate on these 10-year bonds is 5.5%, how much is the bond worth today?

What is the present value of the following cash flow stream at a rate of 6.25%?

If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate.

Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value.

Which of the following statements is CORRECT?

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account?

Which of the following bank accounts has the lowest effective annual return?

Your uncle is about to retire, and he wants to buy an annuity that will provide him with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost him to buy the annuity today?

You deposit $500 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?

A "growing annuity" is any cash flow stream that grows over time.

If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series.

Your grandmother just died and left you $100,000 in a trust fund that pays 6.5% interest. You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?

Pasco Co. borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pasco have to pay in a 30-day month?

A $150,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT?

A time line is not meaningful unless all cash flows occur annually.

Midway through the life of an amortized loan, the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal. This is true regardless of the original life of the loan or the interest rate on the loan.

You want to go to Europe 5 years from now, and you can save $3,100 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now?

A time line is meaningful even if all cash flows do not occur annually.

Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years. How much interest would you have to pay in the first year?