Question

Patricia made equal deposits at the beginning of every 3 months into an RRSP. At the end of 6 years, the fund had an accumulated value of $55,000. If the RRSP was earning 4.75% compounded monthly, what was the size of the quarterly deposits? Round to the nearest cent

Answer 1

To calculate the size of the quarterly deposits, we can use the future value formula for an annuity. Using the given information and solving the equation, the size of the quarterly deposits is approximately $155.96.

Step-by-step explanation:

To calculate the size of the quarterly deposits, we need to use the formula for the future value of an annuity. The formula is given by:

FV = P * ((1+r)^n - 1) / r

Where FV is the future value, P is the quarterly deposit, r is the interest rate per period, and n is the number of periods.

In this case, we have FV = $55,000, r = 4.75% / 12 = 0.0039583 (monthly rate), and n = 6 years * 12 months/year = 72 months.

Substituting the values into the formula, we can solve for P:

$55,000 = P * ((1 + 0.0039583)^72 - 1) / 0.0039583

Simplifying the equation gives us:

P * (1.0039583^72 - 1) = $55,000 * 0.0039583

P * 1.3944355 = $217.67

Dividing both sides of the equation by 1.3944355 gives us:

P = $217.67 / 1.3944355

P ≈ $155.96

Therefore, the size of the quarterly deposits was approximately $155.96.