Question

How many years would it take $1,000 to grow to $5,000 assuming an annual interest rate of 15%?

Answer 1

Given. P= $1000

A = $5000

i = 15% or .15

Formula used :

A = Pe^rt

where, A = Amount

P = Principal

e = euler's number

r = rate of interest

t = time in years

Thus, 5000 = 1000e^.15t

e^.15t = 5000 / 1000

e^.15t = 5

Taking natural log of both sides, we get

ln e^.15t = ln 5

0.15t = ln 5

Thus, taking the value of ln 5 = 1.609, and substituting

0.15t = 1.609

t = 1.609 / .15

= 10.73

Thus it would take 10.73 years for $1000 to grow to $5000 at an annual interest rate of 15%.