Question

Shanice invests $5,887 in a retirement account with a fixed annual interest rate of 4% compounded 12 times per year. How long will it take for the account balance to reach $10,296.62?

Answer 1

It takes 14 years for the account balance to reach $10,296.62

Explanation:

Given:

Principal amount = $5,887

Rate of interest = 4% and 12 times per year

Balance amount = $10296.62

To find:

The time to reach $10,296.62 = ?

Solution:

We know that

`N(t) = N_0e^(rt)`

Here,

N(t) = 10,296.62

`N_0`= $5,887

r = 4 % = 0.04

we have to find the t value

On substituting the given values

`10,296.62 = 5,887e^(0.04t)`

Taking ln to remove e we get

ln
`ln(10,296.62) = ln(5887)({0.04t)`

`ln((10296.62)/(5887)) = 0.04t`

ln(1.749) = 0.04t

`t = (ln(1.749))/(0.04)`

`t =( 0.5590)/(0.04)`

t = 13.97

t = 14