It is now January 1, 2018, and you will need $1,000 on January 1, 2022, in 4

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Question:

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 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?

g. What is the EAR, or EFF%, earned on the bank account in part f? What is the APR earned on the account?