Calculate the present value of an investment that will be worth $$\$ 1,000$$ at the stated interest rate after the stated amount of time. 10 years, at \(5.3 \%\) per year, compounded quarterly

For what kind of compound interest investments is the effective rate greater than the nominal rate? When is it smaller? Explain your answer.

Inflation is running \(1 \%\) per month when you deposit $$\$ 10,000$$ in an account earning \(8 \%\) compounded monthly. In constant dollars, how much money will you have two years from now? HINT [See Exercise 41.]

You take out a 2-year, \(\$ 5,000\) loan at \(9 \%\) interest with monthly payments. The lender charges you a \(\$ 100\) fee that can be paid off, interest free, in equal monthly installments over the life of the loan. Thinking of the fee as additional interest, what is the actual annual interest rate you will pay?

Are based on the following chart, which shows monthly figures for Apple Inc. stock in \(2008 .^{14}\) Marked are the following points on the chart: $$\begin{array}{|c|c|c|c|c|c|} \hline \text { Jan. 2008 } & \text { Feb. 2008 } & \text { Mar. 2008 } & \text { Apr. 2008 } & \text { May 2008 } & \text { June 2008 } \\ \hline 180.05 & 125.48 & 122.25 & 153.08 & 183.45 & 185.64 \\ \hline \text { July 2008 } & \text { Aug. 2008 } & \text { Sep. 2008 } & \text { Oct. 2008 } & \text { Nov. 2008 } & \text { Dec. 2008 } \\ \hline 172.58 & 169.55 & 160.18 & 96.80 & 98.24 & 94.00 \\ \hline \end{array}$$ Did Apple's stock undergo compound interest change in the period January through April? (Give a reason for your answer.)

You take out a 15 -year mortgage for \(\$ 50,000\). at \(8 \%\), to be paid off monthly. Construct an amortization table showing how much you will pay in interest each year, and how much goes toward paying off the principal. HINT [See Example 7.]