Question

Maria contributed $100 from her paycheque at the beginning of every month from age 18 to 65 into RRSP account (no contribution on the month of her 65-th birthday). Anna contributed $4000 at the beginning of every year from age 35 to 55 into a similar RRSP account, then left the money in the fund to accumulate for another 10 years (no contribution in the year of her 55-th birthday). Money earned 4.8% compounded daily in both RRSP accounts.

(i) Who had a greater accumulated value, and by how much, when they retired at age 65?
(ii) Calculate how much interest both Maria and Anna earned in their RRSP accounts, respectively.

Answer 1

(a)

Maria:

Maria makes equal monthly contributions worth $ 100 each the beginning of every month starting from her 18th birthday and leading up to her 65th birthday (but excluding the 65th birthday)

Interest Rate = 4.8 % compounded daily

Applicable Daily Interest Rate = 4.8 / 365 = 0.0132 %

Equivalent Monthly Rate = [1+(0.000132)]^(365/12) - 1= 0.004023 or 0.4023 %

Total Number of Monthly Deposits = 12 x (65-18) = 564 months

Accumulated Value of Deposits at age 65 = 100 x (1.004023)^(564) + 100 x (1.004023)^(563) + ...........+ 100 x (1.004023)^(2) + 100 x (1.004023) = 100 x (1.004023) x [{(1.004023)^(564) - 1} / {1.004023 - 1}] = $ 215268.3

Anna:

Anna makes equal annual beginning of year deposits worth $ 4000 each between age 35 and 55 (excluding 55).

Number of Deposits = 55 - 35 = 20

Interest Rate = 4.8 % compounded daily

Equivalent Annual Rate = [1+(0.048/365)]^(365) - 1 = 0.04934 or 4.934 %

Accumulated Value of Deposits at age 65 = (1.04934)^(10) x 4000 x (1.04934)^(20) + 4000 x (1.04934)^(19) + .............+ 4000 x (1.04934)^(2) + 4000 x (1.04934) = 4000 x (1.04934) x [{(1.04934)^(20) - 1} / {1.04934 - 1}] x (1.04934)^(10) = $ 223096.1

As is observable, Anna has a greater accumulated value at age 65 as compared to MAria.

(b) Maria's accumulated Interest = 215268,3 - 100 x 564 = $ 158868.3

Anna's accumulated Interest = 223096.1 - 4000 x 20 = $ 143096.1