## TIME VALUE OF MONEY

TIME VALUE OF MONEY. It is now January 1, 2018, and you will need \$1,000 on January 1, 2022, in 4 years. Your bank compounds interest at an 8% annual rate.

a. How much must you deposit today to have a balance of \$1,000 on January 1, 2022?

b. If you want to make four equal payments on each January 1 from 2019 through 2022

to accumulate the \$1,000, how large must each payment be? (Note that the payments

begin a year from today.)

c. If your father offers to make the payments calculated in part b (\$221.92) or to give you \$750 on January 1, 2019 (a year from today), which would you choose? Explain.

d. If you have only \$750 on January 1, 2019, what interest rate, compounded annually for 3 years, must you earn to have \$1,000 on January 1, 2022?

e. Suppose you can deposit only \$200 each January 1 from 2019 through 2022 (4 years). What interest rate, with annual compounding, must you earn to end up with \$1,000 on January 1, 2022?

f. Your father offers to give you \$400 on January 1, 2019. You will then make six additional equal payments each 6 months from July 2019 through January 2022. If your bank pays 8% compounded semiannually, how large must each payment be for you to end up with \$1,000 on January 1, 2022?

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