Find the present value of the given investment. An investment earns \(10 \%\) per year and is worth \(\$ 5,000\) after 3 months.

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: $$\begin{array}{|c|c|c|c|c|c|} \hline \text { Jan. 2008 } & \text { Feb. 2008 } & \text { Mar. 2008 } & \text { Apr. 2008 } & \text { May 2008 } & \text { June 2008 } \\ \hline 180.05 & 125.48 & 122.25 & 153.08 & 183.45 & 185.64 \\ \hline \text { July 2008 } & \text { Aug. 2008 } & \text { Sep. 2008 } & \text { Oct. 2008 } & \text { Nov. 2008 } & \text { Dec. 2008 } \\ \hline 172.58 & 169.55 & 160.18 & 96.80 & 98.24 & 94.00 \\ \hline \end{array}$$ Suppose you bought Apple stock in January 2008 . If you later sold at one of the marked dates on the chart, which of those dates would have given you the largest annual return (assuming annual compounding), and what would that return have been?

During a prolonged recession, property values on Long Island depreciated by $2 \%$ every 6 months. If my house cost $$\$ 200,000$$ originally, how much was it worth 5 years later?

You take out a 3-year, \(\$ 7,000\) loan at \(8 \%\) 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?

Interpreting the News You hear the following on your local radio station's business news: "The economy last year grew by \(1 \%\). This was the second year in a row in which the economy showed a \(1 \%\) growth." This means that, in dollar terms, the economy grew more last year than the year before. Why?

Calculate the present value of an investment that will be worth $$\$ 1,000$$ at the stated interest rate after the stated amount of time. 4 years, depreciating \(5 \%\) each year