Question

A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double?

Compound interest formula:mc009-1.jpg

t = years since initial deposit
n = number of times compounded per year
r = annual interest rate (as a decimal)
P = initial (principal) investment
V(t) = value of investment after t years
5.9 years
6.1 years
23.4 years
24.5 years

Answer 1

We need 2P = P(1 + r/n)^{nt} with r = 0.12 and n = 4. So

1.03^{4t} = 2 ⇒ 4t ln(1.03) = ln 2 ⇒ t = ln 2 / (4 ln 1.03).

Compute: t ≈ 0.693147 / (4·0.029559) ≈ 0.693147 / 0.118235 ≈ 5.86 ≈ 5.9 years.

Answer: 5.9 years.