Sally contributed $500 every six months for fourteen years into an RRSP earning interest at 7.5% compounded semi-annually. Seven years after the last contribution Sally converted the RRSP into an RRIF which is to pay her equal quarterly payments for sixteen years. If the first payment is due three months after the conversion into the RRIF and the interest on the RRIF is 9% compounded quarterly, how much will Sally receive every three months?

Question

Sally contributed $500 every six months for fourteen years into an RRSP earning interest at 7.5% compounded semi-annually. Seven years after the last contribution Sally converted the RRSP into an RRIF which is to pay her equal quarterly payments for sixteen years. If the first payment is due three months after the conversion into the RRIF and the interest on the RRIF is 9% compounded quarterly, how much will Sally receive every three months?

Answer 1

To determine how much Sally will receive every three months from her RRIF, we need to follow a series of steps.

Step 1: Calculate the future value of Sally's contributions in the RRSP after 14 years.
Using the formula for future value of a lump sum:
FV = P * (1 + r/n)^(nt)
Where:
P = the principal amount (the amount contributed each period)
r = the interest rate per period
n = the number of compounding periods per year
t = the number of years

In Sally's case, P = $500 every six months, r = 7.5% = 0.075, n = 2 (semi-annual compounding), and t = 14 years.

Using these values, we can calculate the future value of Sally's contributions in the RRSP after 14 years.

FV = $500 * (1 + 0.075/2)^(2 * 14)
FV ≈ $17,285.66

So, Sally's contributions will grow to approximately $17,285.66 after 14 years.

Step 2: Calculate the present value of Sally's RRIF payments for 16 years.
Since Sally wants to receive equal quarterly payments from her RRIF for 16 years, we need to calculate the present value of those payments using the formula for present value of an annuity due:
PV = P * [(1 - (1 + r)^(-n))/(r * (1 + r))]

Where:
P = the payment amount
r = the interest rate per period
n = the total number of payment periods

In Sally's case, P is what we need to calculate, r = 9% = 0.09, and n = 16 years * 4 quarters = 64 quarters.

Using these values, we can calculate the present value of Sally's RRIF payments.

PV = P * [(1 - (1 + 0.09)^(-64))/(0.09 * (1 + 0.09))]
PV ≈ P * 8.66797

Step 3: Calculate the quarterly payment amount (P).
Since Sally contributed the same amount every six months, we need to convert the quarterly payment amount to match the semi-annual contributions.

P = $17,285.66 / 2 = $8,642.83

So, Sally will receive approximately $8,642.83 every three months from her RRIF.

Please note that the calculations may vary slightly depending on rounding.