Answer to Question #153103 in Economics of Enterprise for Arsa

Question

A health club offers you a special low membership rate of $29 per month for a
“guaranteed no price increase” period of 100 months. The manager of the club tells
you proudly that “this $29 a month for a lifetime membership is less expensive than a
major medical treatment for heart disease costing $4,000 one hundred months from
now.” If your personal interest rate is 9% (APR) compounded monthly, is the
manager correct in his statement?

Answer 1

$P=\$29, r=9/12=0.75\%, n=100 months$

Future Value, $FV=P \times \frac{[(1+r)^{n}-1]}{r}$ $=29\times \frac{[(1+0.0075)^{100}-1]}{0.0075}= \$4296.19$

So, the future value after 100 months of $\$29$ per month is $\$4296.19$ which is more than the cost of treatment of $\$4,000.$ Hence the manager is wrong in his statement.