Question

Sophie 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 $40,000. If the RRSP was earning 3.25% compounded monthly, what was the size of the quarterly deposits?

Answer 1

first we have to calculate quarterly rate for monthly compounding

EAR = (1+(r/n))^n - 1

r = annual rate

n = compounding periods

let ' x' be quarterly rate

(1 + (3.25%/12))^12 - 1 = (1 + x)^4 - 1

quarterly rate(x) = 0.815%

future value of annuity due = P*[(1+r)^n - 1 / r ]*(1+r)

where P = quarterly deposits

r = rate of interest per quarter = 0.815%

n = number of quarters = 6*4 = 24

40,000 = P*[(1+0.815%)^24 - 1 / 0.815% ]

P = $1503.54

Quarterly deposits = $1503.54