Question

Two annuities are available for purchase that your client has identified. The first annuity pays $2,400 each month over a 4 year period at a nominal rate of 11% p.a. The second annuity pays $15,000 each six-month period, again over 4 years, at a nominal rate of 12% p.a., but has an annual fee of $500, paid at the beginning of each year. Identify which of the two annuities would be a better option for your client.

Answer 1

Annuity One:

Pays $ 2400 per month over a period of four years (48 months) at a nominal rate of 11 % per annum

Applicable nominal interest rate = 11/12 = 0.9167 % per month

PV(Present Value) of the monthly annuities = 2400 x (1/0.009167) x [1-{1/(1.009167)^(48)}] = $ 92858.71

Annuity Two:

Pays $ 15000 every 6 months over 4 years (8 half-years) at a nominal rate of 12 % per annum

$ 500 is paid at annual fees at the beginning of each year. This implies that cash outflow of $ 500 occurs at the end of Year 0(current time/beginning of year 1), Year 1, Year 2 and Year 3.

Applicable Interest Rate = 12/2 = 6 % per half-year (for annuities)

PV of Cash Outflows (annual fees) = 500 + 500 x (1/0.12) x [1-{1/(1.12)^(3)}] = $ 1700.92

PV of Cash Inflows(Semi-Annual Annuity) = 15000 x (1/0.06) x [1-{1/(1.06)^(8)}] = $ 93146.91

Net PV of Cash Inflow = 93146.91 - 1700.92 = $ 91445.99

As Annuity One has a better present value of cash inlfow than Annuity One the same should be selected.