Time value of money Answer the following questions:
a. Find the FV of $\$ 1,000$ after 5 years earning a rate of 10 percent annually.
b. What would the investment's FV be at rates of 0 percent, 5 percent, and 20 percent after $0,1,2,3,4,$ and 5 years?
c. Find the PV of $\$ 1,000$ due in 5 years if the discount rate is 10 percent.
d. What is the rate of return on a security that costs $\$ 1,000$ and returns $\$ 2,000$ after 5 years?
e. Suppose California's population is 30 million people, and its population is expected to grow by 2 percent annually. How long would it take for the population to double?
f. Find the PV of an ordinary annuity that pays $\$ 1,000$ each of the next 5 years if the interest rate is 15 percent. What is the annuity's FV?
g. How would the $P V$ and $F V$ of the above annuity change if it were an annuity due?
h. What would the $\mathrm{FV}$ and the $\mathrm{PV}$ be for $\$ 1,000$ due in 5 years if the interest rate were 10 percent, semiannual compounding?
i. What would the annual payments be for an ordinary annuity for 10 years with a PV of $\$ 1,000$ if the interest rate were 8 percent? What would the payments be if this were an annuity due?
j. Find the PV and the FV of an investment that pays 8 percent annually and makes the following end-of-year payments:
$$\begin{array}{cccc}
0 & 1 & 2 & 3 \\
\hline & \$ 100 & \$ 200 & \$ 400
\end{array}$$
k. Five banks offer nominal rates of 6 percent on deposits, but A pays interest annually, B pays semiannually, C quarterly, D monthly, and E daily.
(1) What effective annual rate does each bank pay? If you deposited $\$ 5,000$ in each bank today, how much would you have at the end of 1 year? 2 years?
(2) If the banks were all insured by the government (the FDIC) and thus equally risky, would they be equally able to attract funds? If not, and the TVM were the only consideration, what nowtinal nate would cause all the banks to provide the same effective annual rate as Bank A?
(3) Suppose you don't have the $\$ 5,000$ but need it at the end of 1 year. You plan to make a series of deposits, annually for A, semiannually for B, quarterly for $C$, monthly for $D,$ and daily for $E,$ with payments beginning today. How large must the payments be to each bank?
(4) Even if the 5 banks provided the same effective annual rate, would a rational investor be indifferent between the banks?
1. Suppose you borrowed $\$ 15,000$. The loan's annual interest rate is 8 percent, and it requires 4 equal end-of-year payments. Set up an amortization schedule that shows the annual payments, interest payments, principal repayments, and beginning and ending loan balances.