You invest $1000 at 5% interest compounded annually. In how many years will you have $2000 in your account?

Problem

If you deposit $1000 into an account paying 5% annual interest compounded yearly, how long until there is $2000 in the account?

Result

It wil take approximately 14 years 2 months and 15 days for the account to go from $1000 to $2000.

Explanation

To find time we use formula:

A=P (1+rn) n⋅t

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

In this example we have

A=$2000, P=$1000, r=5% and n=1

After plugging the given information

0.05 1·t 2000=1000 1 + 1

2000 = 1000 · (1.05) 1·t (1.05) 1·t = 2000

1000

(1.05) 1·t = 2 Take the natural logarithm of both sides

ln 1.051·t = ln (2) 1 · t · ln (1.05) = ln (2)

1·t = ln (2) ln (1.05)

1 · t = 14.2067

t = 14.2067 years = 14 years 2 months and 15 days