Suppose you have a choice of two equally risky annuities, each paying $1,000 per year for 20 years with similar interest rates. One is an annuity due, while the other is an ordinary annuity. Which annuity would you choose

Annuity due would be be chosen.

Explanation:

Let us assume the similar annual interest rate is 10%.

To decide which to choose, the present values of the two annuities are calculated and compared as follows:

1. For annuity due

Under an annuity due, payments are made to investors at the beginning of each time period. The present value of an annuity due can be calculated as follows:

PVd = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] × (1+r) (1)

Where;

PVd = Present value of an annuity due = ?

P = Annual payment = $1,000

r = interest rate = 10%, or 0.10

n = number of years = 20

Substituting the values into equation (1) above, we have:

PVd = $1,000 × [{1 - [1 ÷ (1 + 0.10)]^20} ÷ 0.10] × (1 + 0.10) = $9,364.92

2. For ordinary annuity

Under an ordinary annuity, payments are made to investors at the end of each time period. The present value of an ordinary annuity can be calculated as follows:

PVd = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] (2)

Where

PVo = Present value of an ordinary annuity = ?

P = Annual payment = $1,000

r = interest rate = 10%, or 0.10

n = number of years = 20

Substituting the values into equation (1) above, we have:

PVo = $1,000 × [{1 - [1 ÷ (1 + 0.10)]^20} ÷ 0.10] = $8,513.56

3. Decision

Since the present value (PV) of the annuity due of $9,364.92 is greater than the PV of ordinary annuity of $8,513.56, annuity due would be be chosen.

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