Omar will contribute $200 to his RRSP at the end of each month for 15 years and then raise his monthly contribution to $500 at the end of each month for the subsequent 20 years. If his investments earn 11.7% compounded monthly, what will be the value of the investments after the last $500 contribution is made 25 years from now?
A) $1,186,877
B) $572,207
C) $1,471,930
D) $521,751
E) $285,054

Question

Quizplus · Accepted Answer

The value of Omar's investments can be calculated using the future value of an annuity formula for each phase of contributions, and then adding the future value of the first phase (after it has grown for the additional 20 years without additional contributions) to the future value of the second phase. First phase (15 years of $200 monthly contributions):$$FV_1 = P \times \frac{(1 + r)^n - 1}{r}$$Where:- $P = \$200$ (monthly contribution)- $r = \frac{11.7\%}{12} = 0.00975$ (monthly interest rate)- $n = 15 \times 12 = 180$ (total number of contributions)$$FV_1 = 200 \times \frac{(1 + 0.00975)^{180} - 1}{0.00975}$$This amount then grows for another 20 years without additional contributions:$$FV_1' = FV_1 \times (1 + r)^{240}$$Second phase (20 years of $500 monthly contributions):$$FV_2 = P \times \frac{(1 + r)^n - 1}{r}$$Where:- $P = \$500$- $n = 20 \times 12 = 240$$$FV_2 = 500 \times \frac{(1 + 0.00975)^{240} - 1}{0.00975}$$The total future value is the sum of $FV_1'$ and $FV_2$. Calculating these values gives a total close to $1,471,930, which matches option C.

Omar Will Contribute $200 to His RRSP at the End