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 or to give you $750 on January 1, 2019 (a year from today), which would you choose? Explain.
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 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 Effective Annual Rate (EAR) earned on the bank account in part f? What is the Nominal Interest Rate or Annual Percentage Rate (APR) earned on the account?
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