Question

Rachel deposited $6,449.82 into a savings account with an interest of 6.9% compounded annually. About how long will it take for the accout to be worth $8,000?

Answer 1

3 years and 3 months.

Explanation:

Since, the amount formula in compound interest,

`A= P(1+(r)/(100))^t`

Where,

P = principal amount,

r = rate per period,

t = number of periods,

Here, A = $ 8,000, r = 6.9%, P = $6,449.82,

By substituting the values,

`8000 = 6449.82(1+(6.9)/(100))^t`

`(8000)/(6449.82)=(1+(6.9)/(100))^t`

`\ln ((8000)/(6449.82))=t\ln(1.069)`

`\implies t = (\ln ((8000)/(6449.82)))/(\ln(1.069))=3.228`

Hence, it would be take 3.228 years or 3 years and 3 months.