Question

Jaidee invests $2,628 in a retirement account with a fixed annual interest rate of 2.33% compounded 12 times per year. How long will it take for the account balance to reach $3,726.18?

Answer 1

The time it will take for the account balance to reach $3,726.18 is 15 months.

Explanation:

The information provided is:

• Jaidee invests $2,628 in a retirement account
• With a fixed annual interest rate of 2.33%
• Compounded 12 times per year, i.e. compounded monthly.
• Final account balance: $3,726.18

The formula of compound interest (compounded monthly) is:

`A=P(1+(r)/(12))^(12t)`

Compute the value of t as follows:

`3726.18=2628* (1+(0.0233)/(12))^(12t)\\\\(3726.18)/(2628)= (1.00194167)^(12t)\\\\1.41787671= (1.00194167)^(12t)\\\\\log(1.41787671)= 12t* \log(1.00194167)\\\\12t=(\log(1.41787671))/(\log(1.00194167))\\\\t=14.99995\\\\t\approx 15`

Thus, the time it will take for the account balance to reach $3,726.18 is 15 months.