Exam 4: Time value of money

Your older brother turned 35 today, and he is planning to save $7, 000 per year for retirement, with the first deposit to be made one year from today.He will invest in a mutual fund that's expected to provide a return of 7.5% per year.He plans to retire 30 years from today, when he turns 65, and he expects to live for 25 years after retirement, to age 90.Under these assumptions, how much can he spend each year after he retires? His first withdrawal will be made at the end of his first retirement year.

As a result of compounding, the effective annual rate on a bank deposit (or a loan)is always equal to or less than the nominal rate on the deposit (or loan).

You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows.Which of the following would lower the calculated value of the investment?

Suppose a State of North Carolina 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?

How much would $100, growing at 5% per year, be worth after 75 years?

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1, 250?

Suppose United Bank offers to lend you $10, 000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10, 000 principal amount at the end of the year.What is the effective annual rate on the loan?

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

How much would $20, 000 due in 50 years be worth today if the discount rate were 7.5%?

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?

You were left $100, 000 in a trust fund set up by your grandfather.The fund 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?

You sold your motorcycle and accepted a note with the following cash flow stream as your payment.What was the effective price you received for the car assuming an interest rate of 6.0%?

You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly.If you invest $3, 000 at the end of each month, how many months will it take for your account to grow to $150, 000?

Cochrane Associate's net sales last year were $525 million.If sales grow at 7.5% per year, how large (in millions)will they be 8 years later?

Which of the following statements regarding a 20-year (240-month)$225, 000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

Which of the following statements is CORRECT?

The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant.

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

A salt mine you inherited will pay you $25, 000 per year for 25 years, with the first payment being made today.If you think a fair return on the mine is 7.5%, how much should you ask for it if you decide to sell it?

Which of the following statements regarding a 15-year (180-month)$225, 000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)