Question

You have $500 in a savings account. How long will it take to double that

amount at an 8% annual interest rate?

Answer 1

Explanation:

The formula for compound annual interest is A = P(1 + r)t where

A = Accumulated or final amount (double $500 = $1000)

P = Principal or original amount ($500)

r = Rate as a decimal (0.08)

t = Time in years

1000 = 500(1 + 0.08)t

2 = 1.08t

Take the logarithm of both sides. I prefer the natural logarithm ln, but if you're more comfortable with base 10 logs they will work just as well

ln(2) = ln(1.08t)

ln(2) = t*ln(1.08)

t = ln(2)/ln(1.08)

t = 9.0065 years

Check: 500*1.089.0065 = $1000