Question

Ali made equal deposits at the beginning of every 3 months into an RRSP. At the end of 8 years, the fund had an accumulated value of $60,000. If the RRSP was earning 4.50% compounded monthly, what was the size of the quarterly deposits?

Answer 1

Answer:

Annual interest rate = 4.50%

Monthly interest rate = 4.50%/12 = 0.375%

Effective annual rate

= (1 + Monthly interest rate)^12 - 1 = (1+0.00375)^12-1 = (1.00375)^12-1 = (1.0459)-1 = 0.0459%

0.0459%

quarterly interest rate

=  (1 + Effective annual rate)^(1/4) - 1 = (1+0.0459)^(1/4)-1 = 1.01128 - 1 = 0.01128 or 1.128%

1.128%

Accumulated sum = $ 60,000

Time period = 8 yrs = 32 quarters.

Let quarterly deposit be $y

$y1.01128^32 + $y1.01128^31 + … + $y1.01128^2 + $y1.01128 = $60,000
$y * 1.01128 * (1.01128^32 - 1) / 0.01128 = $60,000
$y * 38.71283 = $60,000
$y = $1,549.87