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.)

Annuity Value _______________

is it 34591.27 or 34591.33 or 34591.35

Answer 1

Step 1 - Find out the future value of $89000 invested in a Land.
We can use the Future value of lumsum formula to calculate this value.
Future value of lumsum = P x (1+g)^n
P = sum invested = $89000
g = growth rate = 13%
n = number of years = 8
Future value of lumsum = 89000 x (1+0.13)^8
Future value of lumsum = 89000 x 2.658444
Future value of lumsum = 236601.53
Hence , proceeds realised on sale of land after 8 years = $2,36,601.53
Step 2 - Find out the 18 year annuity which is having present value equivalent to value calculated in Step 1.
We can use the present value of annuity formula to calculate this annuity.
Present value of annuity = A x {[1 - (1+r)^-n]/r}
Present value of annuity = 236601.53
A = annuity = ?
r = interest rate per year = 13%
n = number of years = 18
236601.53 = A x {[1 - (1+0.13)^-18]/0.13}
236601.53 = A x 6.839905
A = 34591.35
Annuity value is $34,591.35