91Ó°ÊÓ

In order to pay for baseball uniforms, a school takes out a simple interest loan for \(\$ 20,000\) for seven months at a rate of \(12 \%\) a. How much interest must the school pay? b. Find the future value of the loan.

The unpaid balance of an installment loan is equal to the present value of the remaining payments. The unpaid balance, \(P\), is given by $$ P=P M T \frac{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}{\left(\frac{r}{n}\right)}, $$

How much should you deposit at the end of each month into an IRA that pays \(6.5 \%\) compounded monthly to have \(\$ 2\) million when you retire in 45 years? How much of the \(\$ 2\) million comes from interest?

In Exercises \(21-34\), express each percent as a decimal. \(62 \frac{1}{2} \%\)

How much should you deposit at the end of each month into an IRA that pays \(8.5 \%\) compounded monthly to have \(\$ 4\) million when you retire in 45 years? How much of the \(\$ 4\) million comes from interest?

To borrow money, you pawn your guitar. Based on the value of the guitar, the pawnbroker loans you \(\$ 960\). One month later, you get the guitar back by paying the pawnbroker \(\$ 1472\). What annual interest rate did you pay?

a. Suppose that between the ages of 25 and 37, you contribute \(\$ 3500\) per year to a \(401(\mathrm{k})\) and your employer matches this contribution dollar for dollar on your behalf. The interest rate is \(8.25 \%\) compounded annually. What is the value of the \(401(\mathrm{k})\), rounded to the nearest dollar, after 12 years? b. Suppose that after 12 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the \(401(\mathrm{k})\). How much money, to the nearest dollar, will you have in the plan when you reach age 65 ? c. What is the difference between the amount of money you will have accumulated in the \(401(\mathrm{k})\) and the amount you contributed to the plan?

To borrow money, you pawn your mountain bike. Based on the value of the bike, the pawnbroker loans you \(\$ 552\). One month later, you get the bike back by paying the pawnbroker \(\$ 851\). What annual interest rate did you pay?

What is the future value of a loan and how is it determined?

Describe the two ways that investors make money with stock.