Question

Suppose a 65-year-old person wants to purchase an annuity from an insurance company that would pay $20,700 per year until the end of that person’s life. The insurance company expects this person to live for 15 more years and would be willing to pay 7 percent on the annuity. How much should the insurance company ask this person to pay for the annuity? b. A second 65-year-old person wants the same $20,700 annuity, but this person is healthier and is expected to live for 20 more years. If the same 7 percent interest rate applies, how much should this healthier person be charged for the annuity?

Answer 1

→Answer:

a. $188,533.82

b. $219,296.09

Explanation:

These problems can be solved using the present value of annuity formula which is:

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

Where:

PV = the present value of annuity (the amount we are solving for)

C= The annual amount receivable from the insurance company ($20,700)

r= The interest rate (7%)

n= Number of years (15 and 20 years respectively)

• To solve the first question (a) plug the variables into the formula and you will have → 20,700 × (1-(1.07)^-15)/.07= $188,533.82
• to solve the second question (b) plug the variables into the formula and you will have → 20,700×(1-(1.07)^-20)/.07 = $219,296.09