Sam was injured in an accident,and the insurance company has offered him the choice of $25,000 per year for 15 years,with the first payment being made today,or a lump sum.If a fair return is 7.5%,how large must the lump sum be to leave him as well off financially as with the annuity?

Question

Quizplus · Accepted Answer

We can use the present value formula to compare the lump sum amount to the annuity payments. Let X be the lump sum amount and PMT be the yearly payment of $25,000. Then we have:

X = PMT*(1 - (1+i)^(-n))/i + (1+i)^(-n)*PMT

where i is the interest rate (7.5% or 0.075), and n is the number of years (15).

Simplifying this formula, we get:

X = 25,000*(1 - 1.075^(-15))/0.075 + 1.075^(-15)*25,000
X = 237,229.09

So the lump sum amount would need to be $237,229.09 to leave Sam as well off financially as the annuity payments. Therefore, option B is the best choice.

Sam Was Injured in an Accident,and the Insurance Company Has