Question

John and Jane will contribute to an RRSP 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 RRSP if they live until their 81, 91 or 101 birthday?

Both John and Jane have 10 000 which they will contribute to their new RRSP on their 31st birthday. Supposing that their RRSPs earn 12% compounded monthly what is John’s monthly contribution if he plans to live until 91? Similarly, what is Jane’s monthly contribution if she plans to live until 101?

Answer 1

a)

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 until the age of 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 until 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 until 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 until 101.

b)

Calculation of Jhon's monthly contribution if he plane to live until the age 91:

Present Value = 10,000

Interest = 12%

Compounded monthly

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

No. of periods = (91-31)*12

= 720

Interest Per period =12%/12

= 1%

10000 = PMT[((1+0.01)^720-1)/(0.01*(1.01)^720)

= PMT[(1292.377-1)/(0.01*1292.377)

= PMT[1291.377/12.9237]

  = PMT*99.92

PMT = 10000/99.92

PMT = $100.08 ( Approx)

Jhon will get a monthly contribution of $100 monthly if he lives until the age 91.

Calculation of Jane's monthly contribution if she plane to live until the age 101:

Present Value = 10,000

Interest = 12%

Compounded monthly

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

No. of periods = (101-31)*12

= 840

Interest Per period =12%/12

= 1%

10000 = PMT[((1+0.01)^840-1)/(0.01*(1.01)^840)

= PMT[(4265.343-1)/(0.01*4265.343)

= PMT[4264.343/42.65]

  = PMT*99.98

PMT = 10000/99.98

PMT = $100.02 ( Approx)

Jane will get a monthly contribution of $100.02 monthly if she lives until the age 101.