Question

Retirement planning.

Both John and Jane have $10,000 which they will contribute to their new RRSPs on their 31^st birthdays. From then on, they will contribute to their RRSPs until they are each 71. 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. 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

Sol - The answer to the above question is as follows -

John's Monthly contribution if he plans to live until 91

We are given,

Present Value = $10,000

RRSP's earn compounded monthly interest of = 12%

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

n or No. of periods = (91 - 31) * 12 = 720

Interest per period will be %1 that is 12%/12.

$10,000 = Monthly payment[(1+0.01)^720-1/0.01*(1.01)^720]

$10,000 = Monthly payment (1291.37 / 12.92)

$10,000 = Monthly Payment * 99.92

Monthly Payment = $10,000/99.92

= $100

Janes's monthly Contribution if she Plans to live until 101

Present Value of Annuity = Monthly Payment[(1+i)^n-1/i(1+i)^n]

n or no. of periods = (101 - 31)*12 = 840

Interest per period is 1% that is 12%/12

$10,000 = Monthly Payment[(1+0.01)^840-1/0.01*(1.01)^840

$10,000 = Monthly Payment[(4265.34-1)/(0.01*4265.34)

$10,000 = Monthly Payment*99.97

Monthly Payment = $10,000/99.97

= $100 approximately

Therefore,John will contribute $100 approximately per month if he lives until 91 and jane will contribute an amount of $100 approximate if she lives until the age of 101