Question

Adrian deposited $400 at the end of every month into an RRSP for 7 years. The interest rate earned was 4.50% compounded semi-annually for the first 4 years and changed to 4.75% compounded monthly for the next 3 years. What was the accumulated value of the RRSP at the end of 7 years? (Round to the nearest cent)

Answer 1

The accumulated value of the RRSP at the end of 7 years is $57,041.41.

Step-by-step explanation:

To calculate the accumulated value of the RRSP, we need to calculate the accumulated value for the first 4 years at an interest rate of 4.50% compounded semi-annually, and then for the next 3 years at an interest rate of 4.75% compounded monthly.

For the first 4 years:

1. The monthly deposits are $400 x 12 = $4,800 per year.
2. The number of semi-annual periods is 4 years x 2 = 8 periods.
3. The interest rate per semi-annual period is 4.50% / 2 = 2.25%.
4. Using the formula for compound interest, the future value of the deposits for the first 4 years is:

FV = $4,800 x ((1 + 0.0225)8 - 1) / 0.0225 = $41,163.46

For the next 3 years:

1. The monthly deposits are $400 x 12 = $4,800 per year.
2. The number of monthly periods is 3 years x 12 = 36 periods.
3. The interest rate per monthly period is 4.75% / 12 = 0.3958%.
4. Using the formula for compound interest, the future value of the deposits for the next 3 years is:

FV = $4,800 x ((1 + 0.003958)36 - 1) / 0.003958 = $15,877.95

To calculate the total accumulated value, we add the future values of the deposits for the first 4 years and the next 3 years:

Total Accumulated Value = $41,163.46 + $15,877.95 = $57,041.41