Answer to Question #215875 in Financial Math for nini

Question

Harry has received a $1,500 bonus. His bonus is expected to grow by 5 percent for the next 5 years. How much will Harry have at the end of the fifth year if he invests his bonuses (including the most recent bonus) in a project paying 8 percent per year?

Answer 1

FV of Growing annuity due $= PMT \times [\frac{((1+r)^n - (1+g)^n) }{(r - g)}] \times (1 +r)$

PV = present value

FV = future value

PMT = payment per period

r = interest rate in percent per period

g= interest rate in percent per period for the bonus.

n = number of periods

$= 1500 \times [\frac{((1 + 0.08)^{5} - (1 + 0.05){5}) }{ (0.08 - 0.05)}] \times (1 + 0.08)\\ = 1500 \times [\frac{( 1469328 - 1.276282) }{ 0.03}] \times 1.08\\ = 1500 \times 6.43488381 \times1.08\\ = 10424.51$