Question

Retirement planning.

John and Jane will each contribute to their RRSPs until they are each 71. When they turn 71, CRA rules require them to switch their RRSPs to an annuity and begin receiving payments. John and Jane will receive their first payments on their (respective) 71st birthdays. Each wish to receive a payment of $10,000 per month until they die. If the annuity pays 5% interest compounded monthly, how much must they have saved in their RRSPs if they live until their 81, 91 or 101 birthday?

Answer 1

Answer :

Amount to be received monthly = $10,000

Interest Rate = 5%

Present value of annuity = PMT [(1+i)^n-1/i(1+i)^n]

Where ,

PMT = Monthly payments

i = Interest per period

n = No.of periods

When he live untill the age 81 :

No. of periods = (81 - 71)*12

= 120 periods

Interest per period = 5%/12

= 0.42%

Present value of annuity = 10000[((1+0.0042)^120 - 1)/(0.0042*(1.0042)^120)

= 10000[(1.6536-1)/(0.0042*1.6536)

= 10000[0.6536/0.0069]

= 10000*94.73

= $9,47,300 (Approx)

John and Jane should save $9,47,300 to get $10000 monthly if they live until 81

When he live untill the age of 91 :

No.of periods = (91-71)*12

= 240 periods

Interest per period =5%/12

= 0.42%

Present value of annuity = 10000[((1+0.0042^240-1)/(0.0042*(1.0042)^240)

= 10000[(2.7343 -1)/(0.0042*2.7343)

= 10000[1.7343/0.0115]

= 10000*150.81

= 15,08,100 (Approx)

John and Jane should save $15,08,100 to get $10000 monthly if they live until 91.

When he live untill the age of 101 :

No . of periods = (101 - 71)*12

= 360 periods

Interest per period = 5%/12

= 0.42%

Present value of annuity = 10000 [((1 + 0.0042)^360-1)/(0.0042*(1.0042^360)

= 10000[(4.5215-1)/(0.0042*4.5215)

= 10000[3.5215/0.0190]

= 10000*185.34

= $18,53,400 (Approx)

John and Jane should save $18,53,400 to get $10000 monthly if they live untill 101.