Question

Howard’s uncle gave him $885 for his tenth birthday. The money was invested in a savings account with interest compounded at 12% semi-annually. He decided to leave the money in the account until it reached an amount of $3500, at which time he will use it as a down payment on a car. How long will it take him?

Answer 1

Principal Amount = P = $885
Amount Accumulated = A = $3500
Interest rate = r = 12% = 0.12
Compounding period in a year = n = 2
Time in years = t = ?

The formula for compounding is:

$A=P(1+ \frac{r}{n})^{t*n}$

Using the values, we get:

$3500=885(1+ \frac{0.12}{2})^{2*t} \\ \\ \frac{3500}{885} =(1.06)^{2t} \\ \\ log(\frac{3500}{885})=log((1.06)^{2t}) \\ \\ log(\frac{3500}{885})=2tlog(1.06) \\ \\ t= \frac{log(\frac{3500}{885})}{2log(1.06)} \\ \\ \\ t=11.80$

This means, it will take him 11.8 or approximately 12 years