Question

Rolfe set up an RRSP for a client when the client was 30 years old. The client put $750 into the account every month until they retired at age 60. The account averaged an annual rate of 7.6% per year compounded annually. If the client then wanted to take a monthly disbursement from the account starting at age 60 for the next 25 years, what would the monthly disbursement be if the RRSP investment retained the same terms and after 25 years would have a zero balance?

Answer 1

The client puts $750 for 30 years before retirement every month where he receives 7.6% per year. The value it must have grown at his retirement = 750*(1+0.076/12)^360 + 750*(1+0.076/12)^359 + 750*(1+0.076/12)^358 + 750*(1+0.076/12)^357 + ----------------- + 750*(1+0.076/12)^1 + 750

Using the GP formula to solve the above equation,

Value at retirement = 750*((1+0.076/12)^360 - 1))/(1+0.076/12) - 1) = 1031049.65

Monthly disbursement is A post-retirement for 25 years with a rate of return 7.6% on the deposited amount.

Using the time value formula for PV of annuity,

1031049.65 = A/(1+0.076/12) + A/(1+0.076/12)^2 + A/(1+0.076/12)^3 + ----------------------+ A/(1+0.076/12)^300

=> 1031049.65 = A{1 - (1+0.076/12)^(-300)}/{0.076/12}

=> A = 7686.558