Question

An investment offers 5,300 per year for 15 years, with the first payment occuring one year from now. if the required return is 7 percent, what is the value of theinvestment? what would the value be if the payments occured for 40 years? for 75 years? forever?

Answer 1

value of investment = ΣA/(1+r)^n from n = 1 to n-1

value of investment = A(1-1/(1+r)^n)/(1-1/(1+r)) = A*((1+r)^n - 1)/r*(1+r)^n-1
case 1
r=.07
A = 5300
n =15
valuee of investment = 5300*(1.07^15-1)/0.07*1.07^14 = 46351

for n = 40

value of investment = 70,304

for n = 75

value of investment = 75207

forever

value of inestment = 75714.3

Answer 2

interest rate i =7%
n=15 years
Captialt C=4600

present value(PV) = C[1-(1+i)^-n]/i

value of investment or PV =5300[1-(1+0.07)^-15]/0.07

=$51004.32

for n=40 years

value of investment =5300[1-(1+0.07)^-40]/0.07 =$70,658.05

for n=75 years

value of investment=5600[1-(1+0.07)^-75]/0.07 =$75,240.7