Question

You are considering the purchase of two different insurance annuities. Annuity A will pay you $16,000 at the beginning of each year for 8 years. Annuity B will pay you $12,000 at the end of each year for 12 years. Assuming your money is worth 7%, and each costs you $75,000 today, which would you prefer?

Answer 1

Answer on Question #50305 – Economics - Finance

You are considering the purchase of two different insurance annuities. Annuity A will pay you $16,000 at the beginning of each year for 8 years. Annuity B will pay you $12,000 at the end of each year for 12 years. Assuming your money is worth 7%, and each costs you $75,000 today, which would you prefer?

Solution

To choose which annuity is better we need to compare its NPV:

$$NPV = \sum_{t=1}^{T} \frac{C_t}{(1 + r)^t} - C_o$$

where:

$C_t$ = net cash inflow during the period

$C_o$ = initial investment

$r$ = discount rate, and

$t$ = number of time periods

$$NPV_A = \sum_{t=0}^{7} \frac{16,000}{(1 + 7\%)^t} - 75,000 = 102,228 - 75,000 = 27,228$$ $$NPV_B = \sum_{t=1}^{12} \frac{12,000}{(1 + 7\%)^t} - 75,000 = 95,312 - 75,000 = 20,312$$

Answer

I would prefer Annuity A, because its NPV is bigger than Annuity B NPV.

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