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

Answer:

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

Step-by-step 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$ln(10,296.62) = ln(5887)({0.04t)$

$ln(\frac{10296.62}{5887}) = 0.04t$

ln(1.749) = 0.04t

$t = \frac{ln(1.749)}{0.04}$

$t =\frac{ 0.5590}{0.04}$

t = 13.97

t = 14