Question

(a) Mary Jane (aged 55) has just started working with the XYZ Company and is just
trying to catch up on having money for retirement. XYZ offers her a pension plan
with an annuity that is guaranteed to earn 10% interest compounded annually.
She plans to work for 5 years before retiring and would then like to be able to
draw an income of $100,000 per annum for 15 years. How much must be
deposited per annum into her retirement fund to accomplish this?

Answer 1

After retirement,

Annual Withdrawal = $100,000

Time Period = 15 years

Interest Rate = 10%

Calculating Present Value of Annuity at retirement,

Present Value of Annuity = P[(1 - (1 + r)^-n)/r]

Present Value = 100,000[(1 - (1.10)^-15)/0.10]

Present Value = $760,608

Before retirement,

Time Period = 5 years

Interest Rate = 10%

Future Value = $760,608

Calculating Annuity Payment,

Annuity Payment = r(FV)/((1 + r)ⁿ - 1)

Annuity Payment = 0.10(760,608)/((1.10)⁵ - 1)

Annuity Payment = $124,585.67