Atlas Insurance wants to sell you an annuity which will pay you $1,600 per quarter for 25 years.You want to earn a minimum rate of return of 6.5 percent.What is the most you are willing to pay as a lump sum today to buy this annuity?

Question

Quizplus · Accepted Answer

We can use the formula for the present value of an annuity to solve for the most you are willing to pay as a lump sum today:

PV = (PMT / r) x (1 - (1 + r)^(-n))

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 periods.

In this case, PMT = $1,600 per quarter, r = 6.5% / 4 = 0.01625, and n = 25 x 4 = 100.

Plugging in these values, we get:

PV = ($1,600 / 0.01625) x (1 - (1 + 0.01625)^(-100))
PV = $78,818.41

Therefore, the most you are willing to pay as a lump sum today to buy this annuity is $78,818.41. The correct answer is C.

Atlas Insurance Wants to Sell You an Annuity Which Will