Question: Following are some compounding and discounting problems:
a. Say $177 grows to $189 over a year at simple interest, that is, one annual payment and no compounding within the year. What is the implied interest rate?
b. Show that the present value of $189 a year from today at the interest rate you computed is $177.
c. At 12 percent simple interest, what does $230 grow to in two years?
d. What is the present value of $350 to be received in two years if the interest rate is 14 percent?
e. You know in advance that the interest rate your funds can earn for the next year is 12 percent, and 6 percent for the year after that. To what value do your funds grow in one year? In two years? f. Same question as the last one, but now next year's interest rate is 6 percent and the following year's is 12 percent. To what value do your funds grow in one year? In two years? Why are both of your answers for the two-year calculation the same?
g. The interest rate is 12 percent per year. What is the present value of $500 to be received in one year? In two years?
h. You somehow know that next year's interest rate is 18 percent and the following year's will be 3 percent. Calculate the present value of $275 to be received two years from today.
i. Find the value of a three-year $45 annuity if the interest rate is 5 percent per year.
j. Find the value of a $70 perpetuity if the interest rate is 12 percent per year.