Question

Morgan Jennings, a geography professor, invests $89,000 in a parcel of land that is expected to increase in value by 13 percent per year for the next eight years. He will take the proceeds and provide himself with a 18-year annuity.

Assuming a 13 percent interest rate, how much will this annuity be? Use Appendix A and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Answer 1

Using Formula:

Amount Invested = $89,000
Annual interest rate = 13%

Value of Land after 8 years = $89,000 * 1.13^8
Value of Land after 8 years = $236,601.53

Present Value of Annuity = $236,601.53
Period of Annuity = 18 years

Annual Annuity Payment = Present Value of Annuity / PVIFA(13%, 18)
Annual Annuity Payment = $236,601.53 / [(1 - (1/1.13)^18) / 0.13]
Annual Annuity Payment = $236,601.53 / 6.8399
Annual Annuity Payment = $34,591.35

Using Financial Calculator:

Amount Invested = $89,000
Annual interest rate = 13%

PV = $89,000
I/Y = 13%
N = 8
FV = 236601.53

Value of Land after 8 years = $236,601.53

Present Value of Annuity = $236,601.53
Period of Annuity = 18 years

PV = $236,601.53
N = 18
I/Y = 13%
PMT = 34591.35

Annual Annuity Payment = $34,591.35

Using Table Values:

Amount Invested = $89,000
Annual interest rate = 13%

Value of Land after 8 years = $89,000 * FVIFA(13%, 8)
Value of Land after 8 years = $89,000 * 2.65844
Value of Land after 8 years = $236,601.16

Present Value of Annuity = $236,601.16
Period of Annuity = 18 years

Annual Annuity Payment = Present Value of Annuity / PVIFA(13%, 18)
Annual Annuity Payment = $236,601.16 / 6.83991
Annual Annuity Payment = $34,591.27