Exam 5: The Time Value of Money

Your retirement account has a current balance of $50,000. What interest rate would need to be earned in order to accumulate a total of $1,000,000 in 30 years, by adding $6,000 annually?

Would a depositor prefer an APR of 8% with monthly compounding or an APR of 8.5% with semiannual compounding?

Show numerically that a savings account with a current balance of $1,000 that earns interest at 9% annually is precisely sufficient to make the payments on a 3-year loan of $1,000 that carries equal annual payments at 9% interest.

Your real estate agent mentions that homes in your price range require a payment of $1,200 per month for 30 years at 9% interest. What is the size of the mortgage with these terms?

Any sequence of equally spaced, level cash flows is called an annuity. An annuity is also known as a perpetuity.

A mortgage loan is an example of an amortizing loan. "Amortizing" means that part of the monthly payment is used to pay interest on the loan and part is used to reduce the amount of the loan.

Miller's Hardware plans on saving $42,000, $54,000, and $58,000 at the end of each year for the next three years, respectively. How much will the firm have saved at the end of the three years if it can earn 4.5% on its savings?

An effective annual rate must be greater than an annual percentage rate.

You will be receiving cash flows of: $1,000 today, $2,000 at end of year 1, $4,000 at end of year 3, and $6,000 at end of year 5. What is the present value of these cash flows at an interest rate of 7%?

A corporation has promised to pay $1,000 20 years from today for each bond sold now. No interest will be paid on the bonds during the 20 years, and the bonds are discounted at an interest rate of 7%, compounded semiannually. Approximately how much should an investor pay for each bond?

What is the present value of the following payment stream, discounted at 8% annually: $1,000 at the end of year 1, $2,000 at the end of year 2, and $3,000 at the end of year 3?

The more frequent the compounding, the higher the future value, other things equal.

The Excel function for future value is FV (rate, nper, pmt, PV).

The Excel function for present value is PV (rate, nper, pmt, FV).

After reading the fine print in your credit card agreement, you find that the "low" interest rate is actually an 18% APR, or 1.5% per month. What is the effective annual rate?

Would you prefer a savings account that paid 7% interest compounded quarterly, 6.8% compounded monthly, 7.2% compounded weekly, or an account that paid 7.5% with annual compounding?

$50,000 is borrowed, to be repaid in three equal, annual payments with 10% interest. Approximately how much principal is amortized with the first payment?

How much interest can be accumulated during one year on a $1,000 deposit paying continuously compounded interest at an APR of 10%?

If a borrower promises to pay you $1,900 nine years from now in return for a loan of $1,000 today, what effective annual interest rate is being offered if interest is compounded annually?

Under which of the following conditions will a future value calculated with simple interest exceed a future value calculated with compound interest at the same rate?