Question

Alonzo deposited into an account with a annual interest rate, compounded monthly. Assuming that no withdrawals are made, how long will it take for the investment to grow to

Answer 1

Answer:

5.42 years

Explanation:

The computation of the number of years is as follows:

As we know that

Future value = Present value × (1 + rate of interest)^number of years

Here we assume the number of years be n

$7,160 = $4,000 × (1 + 0.108 ÷ 12)^12n

$7,160 ÷ $4,000 = (1 + 0.108 ÷ 12)^12n

$7,160 ÷ $4,000 = (1.009)^12n

Now take the log to the both sides

log $7,160 ÷ $4,000 = log (1.009)^12n

log $716 ÷ $400 = 12 t log 1.009

t = log ($716 ÷ $400) ÷ 12 t log 1.009

= 5.42 years