Question

1. Futures values: If you invest $1,000 at an interest rate of 12%, how much will you have at the end of eight years? Present values: As winner of a breakfast cereal competition, you can choose one of the following prizes: a. $10,000 now. b. $18,000 at the end of five years. c. $1,140 a year forever. d. $1,900 for each of 10 years. e. $650 next year and increasing thereafter by 4% a year forever. If the interest rate is 8%, which is the most valuable prize?

Answer 1

Answer 1
Future Value
Future value of sum = P x (1+r)^n
P = sum invested = $1000
r = interest rate per year = 12%
n = number of years = 8
Future value of sum = 1000 x (1+0.12)^8
Future value of sum = 2475.96
You will have $2475.96 at the end of eight years.
Answer 2
Option a
Present value of Option a = $10,000
Option b
Present value of sum = P x (1+r)^-n
Present value of sum = $18000 x (1+0.08)^-5
Present value of Option b = $12,250.50
Option c
Present value of Option c = $1140 / 8% = $14,450
Option d
Present Value of annuity = P x {[1 - (1+r)^-n]/r}
Present Value of annuity = $1900 x {[1 - (1+0.08)^-10]/0.08}
Present Value of annuity = $1900 x 6.710081
Present value of Option d = $12,749.15
Option e
Present value of growing annuity = P / (r - g)
Present value of growing annuity = $650 / (0.08 - 0.04)
Present value of Option e = $16,250
The answer is : Option e is the most valuable prize.