Question

An insurance company wants to sell you an annuity which will pay you $750 per quarter for 30 years. You want to earn a minimum rate of return of 6.0 percent. What is the most you are willing to pay as a lump sum today to buy this annuity

Answer 1

$41,623.84

Step-by-step explanation:

`\text{Present Lump\: Sum}, \:A_0=(P[1-(1+i)^(-kt)])/((r)/(k) )`

C=Payment Per Period

Yearly Interest Rate, =6%=0.06

Therefore, Periodic(Quaterly) Interest Rate, i= 0.06/4=0.015

Total number of Periods, n =4 X 30 =120 Quarters

Therefore, the maximum lump sum that the client will be willing to pay is:

`=(750[1-(1+0.015)^(-4X30)])/(0.015)=\$41,623.84`