Exam 5: Time Value of Money

For any interest rate and for any period of time, the more frequently interest is compounded, the greater the amount of money that has to be invested today in order to accumulate a given future amount.

The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of the next 10 years is ________.

In general, with an amortized loan, the payment amount remains constant over the life of the loan, the principal portion of each payment declines over the life of the loan, and the interest portion of each payment grows over the life of the loan.

A generous philanthropist plans to make a one-time endowment to a renowned heart research center which would provide the facility with $250,000 per year into perpetuity. The rate of interest is expected to be 8 percent for all future time periods. How large must the endowment be?

Jia has just won a $20 million lottery, which will pay her $1 million at the end of each year for 20 years. An investor has offered her $10 million for this annuity. She estimates that she can earn 10 percent interest, compounded annually, on any amounts she invests. She asks your advice on whether to accept or reject the offer. What will you tell her? (Ignore Taxes)

The nominal and effective rates are equivalent for annual compounding.

Hayley makes annual end-of-year payments of $6,260.96 on a five-year loan with an 8 percent interest rate. The original principal amount was ________.

Adam borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year payment is ________.

The future value of a $10,000 annuity due deposited at 12 percent compounded annually for each of the next 5 years is ________.

When computing an interest or growth rate, the rate will decrease with an increase in future value, holding present value and the number of periods constant.

An ordinary annuity is an annuity in which cash flows occur at the beginning of each period.

Find the future value at the end of year 3 of the following stream of cash flows received at the end of each year, assuming the firm can earn 8 percent on its investments.

The annual percentage rate (APR) is the nominal rate of interest, found by multiplying the periodic rate by the number of periods in one year.

Calculate the future value of $6,490 received today and deposited for five years in an account which pays interest of 14 percent compounded semiannually.

A local bank is offering a zero-coupon certificate of deposit for $25,000. At maturity, three years from now, the investor will receive $32,000. What is the rate of return on this investment?

The New York Soccer Association would like to accumulate $10,000 by the end of 4 years from now to finance a big soccer weekend for its members. The Association currently has $2,500 and wishes to raise the balance by arranging annual fund-raising events. How much money should they raise at each annual fund-raising event assuming 8 percent rate of interest?

Calculate the present value of $800 received at the beginning of year 1, $400 received at the beginning of year 2, and $700 received at the beginning of year 3, assuming an opportunity cost of 9 percent.

The future value of an annuity of $1,000 each quarter for 10 years, deposited at 12 percent compounded quarterly is ________.

A generous benefactor to a local ballet plans to make a one-time endowment that would provide the ballet with $150,000 per year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment be?

Calculate the future value of $4,600 received today if it is deposited at 9 percent for three years.