Question

a. Suppose a 65-year-old person wants to purchase an annuity from an insurance company that would pay $20,600 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 8 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 $20,600 annuity, but this person is healthier and is expected to live for 20 more years. If the same 8 percent interest rate applies, how much should this healthier person be charged for the annuity?
c. In each case, what is the new purchase price of the annuity if the distribution payments are made at the beginning of the year?

(For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))
  

	a. Purchase price of the annuity b. Purchase price of the annuity c. 15-year purchase price 20-year purchase price

Answer 1

a

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 20600*((1-(1+ 8/100)^-15)/(8/100))

PV = 176325.26

b

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 20600*((1-(1+ 8/100)^-20)/(8/100))

PV = 202253.84

c

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 20600*((1-(1+ 8/100)^-15)/(8/100))*(1+8/100)

PV = 190431.28

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 20600*((1-(1+ 8/100)^-20)/(8/100))*(1+8/100)

PV = 218434.14