Good Life Insurance wants to sell you an annuity which will pay you £500 per quarter for 25 years. You want to earn a minimum rate of return of 5.5%.What is the most you are willing to pay as a lump sum today to buy this annuity?

Question

Quizplus · Accepted Answer

To find the present value of an annuity, we use the formula PV = PMT × [(1 - (1 + r)^-n) / r], where PV is the present value, PMT is the payment per period, r is the interest rate per period, and n is the total number of payments. Given that the payments are £500 per quarter for 25 years (100 quarters) and the annual interest rate is 5.5% (or 0.055), the quarterly interest rate is 0.055/4 = 0.01375. Plugging these values into the formula gives us the maximum amount one should be willing to pay for the annuity to achieve at least a 5.5% rate of return. Calculating with the given values results in a present value of approximately £27,082.94, making option B the correct choice.

Good Life Insurance Wants to Sell You an Annuity Which