Question

1. What is the future worth of the following series of payments? (show all work)

1. $7,000 at the end of each year for 20 years at 6.45% compounded annually. (7 points)

2. $4,000 at the end of each year for 12 years at 7.75% compounded annually. (7 points)

Answer 1

Answer

(a)

Future value of a periodic payment is given by :

FV = (P/r)((1 + r)ⁿ - 1)

where P = Periodic payment = 7000 , r = interest rate = 6.45% = 0.0645 and n = time = 20

=> FV = (P/r)((1 + r)ⁿ - 1) = (7000/0.0645)((1 + 0.0645)²⁰ - 1)

=> FV = 270309.216

Hence, Future Value = $270309.22.

(b)

Future value of a periodic payment is given by :

FV = (P/r)((1 + r)ⁿ - 1)

where P = Periodic payment = 4000 , r = interest rate = 7.75% = 0.0775 and n = time = 12

=> FV = (P/r)((1 + r)ⁿ - 1) = (4000/0.0775)((1 + 0.0775)¹² - 1)

=> FV = 74792.499

Hence, Future Value = $74792.50