Question

7400 dollars is placed in an account with an annual interest rate of 7%. To the nearest

tenth of a year, how long will it take for the account value to reach 36000 dollars?

Answer 1

23.4 years.

Explanation:

7400 dollars is placed in an account with an annual interest rate of 7%.

Now, let us assume that the interest is compounded annually and it will take x years for account value to reach 36000 dollars.

Hence, from the formula of compound interest, we can write that

`36000 = 7400(1 + (7)/(100))^(x)`

⇒
`(1.07)^(x) = 4.865`

Taking ln both sides we get,

x ln (1.07) = ln (4.865)

⇒ x = 23.4 years.