Present Value?

Question

Find the present Value and future value of an income stream of $1000 a year, for a period of 5 years, if the interst rate is 8%

Answer 1

Present value= A[1+r]^-1+A[1+r]^-2+...=A[1-[1+r]-5]/[1-[1+r]^-1]
=A{[(1+r)^5-1]/[1+r]^5}/[r/[r+1]]
=A{[r+1]/r}{1-1/[1+r]^5}
=1000[1.08/.08][1-1/1.08^5]
=13500[1-1/1.469]
=13500*.3194
=4312.12
future value
=1000{[1.08+1.08^2+1.08^3+1.08^4+1.08^5}
=1000[1.08+1.1664+1.2597+1.3604+1.4692]
=1000*6.3357
=6335.7

Answer 2

You use the sum of a geometric series here. You get 1000( 1.08 - 1.08^6)/(1 - 1.08) = 6335.93. That's the future value if 0 is the present value.