Question

$4000 is deposited in an account that pays APR of 7.4% compounded annually. How long will it take for the balance to reach $140,000

Answer 1

It will take 49.8 years.

The equation for compound interest is


`A=p(1+r)^t`,

where A is the total amount in the account, p is the amount of principal invested, r is the interest rate as a decimal, and t is the amount of time. Substituting our information, we have:


`140000=4000(1+0.074)^t \\ \\140000=4000(1.074)^t`

Dividing both sides by 4000, we have:

`(140000)/(4000)=(4000(1.074)^t)/(4000) \\ \\35=1.074^t`

We will use logarithms to undo the exponent:

`log_(1.074)35=t \\ \\49.8=t`