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+ (r)/(n))^(t*n)`

Using the values, we get:


`3500=885(1+ (0.12)/(2))^(2*t) \\ \\ (3500)/(885) =(1.06)^(2t) \\ \\ log((3500)/(885))=log((1.06)^(2t)) \\ \\ log((3500)/(885))=2tlog(1.06) \\ \\ t= (log((3500)/(885)))/(2log(1.06)) \\ \\ \\ t=11.80`

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