Question

Alexa has contributed $2,352.00 every month for the last 11 years into an RRSP fund. The interest eamed by these deposits was 5% compounded monthly for the first 6 years and 7% compounded monthly for the last 5 years. How much money is currently in the RRSP? The balance is $ (Round the final answer to the nearest cent as needed. Round intermediate values to four decimal places as needed.)

Answer 1

Alexa's total amount in the RRSP is found by calculating the future value of monthly contributions for the first 6 years with a 5% compound interest rate and for the last 5 years with a 7% interest rate, compounded monthly. These amounts are then added together to determine the RRSP's current value.

Step-by-step explanation:

The problem presented is a classic example of calculating the future value of annuities with changing interest rates. The question asks us to find out how much money Alexa has in her RRSP (Registered Retirement Savings Plan) after making consistent monthly contributions over a period of 11 years with two different compound interest rates. During the first 6 years, the fund grew with a compound interest rate of 5%, compounded monthly. For the last 5 years, the rate was 7%, also compounded monthly. To determine the total amount in the RRSP, we must calculate the future value of the monthly contributions separately for each interest rate period and then sum the two. We will use the formula for the future value of an annuity compounded monthly:

FV = P × { { (1 + r)n - 1 } / r }

where:

• P is the regular monthly contribution
• r is the monthly interest rate (annual rate divided by 12)
• n is the total number of contributions (months)

Using this formula, we calculate the future value for each period, add them together, and round to the nearest cent to find the total amount in Alexa's RRSP.