John and Jane will contribute
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 toan annuity and begin receiving payments. John and Jane will receivetheir first payments on their (respective) 71st birthdays. Eachwish to receive a payment of $10 000 per month until they die. Ifthe annuity pays 5% interest compounded monthly, how much must theyhave saved in their RRSP if they live until their 81, 91 or 101birthday?
Both John and Jane have 10 000 which they will contribute totheir new RRSP on their 31st birthday. Supposing that their RRSPsearn 12% compounded monthly what is John’s monthly contribution ifhe plans to live until 91? Similarly, what is Jane’s monthlycontribution if she plans to live until 101?
Answer:
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 ifthey 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 ifthey 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 ifthey live until 101.
b)
Calculation of Jhon’s monthly contribution if he planeto 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 livesuntil the age 91.
Calculation of Jane’s monthly contribution if she planeto 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 shelives until the age 101.
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