13. 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

The present value of Annuity is 102,228 which is higher than that of Annuity B - $95,312 Hence, Annuity is preferable.

Explanation:

To determine which to go for, we would calculate the present value of insurance investment discounted at the at the rate of 7%.

The PV of the insurance annuities would be done as follows:

PV of annuity A

The number of payments would be 20 installments. Please be mindful not to say 19. Remember the first the payment occurs in year 4 which is inclusive.

PV = A +  A × 1- ( (1+r)^(-n))/r

A- annual payment

r- rate of return

n- number of years

PV = 16,000 + 16,000 × (1- 1.07^(-7) )/0.07 =  $102,228.63

PV of annuity B

PV = 12,000× (1-1.07^(-12)/0.07) =  $95,312.24

The present value of Annuity is 102,228 which is higher than that of Annuity B - $95,312 Hence, Annuity is preferable.

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