Question

What is the future value of an ordinary annuity of 1000 USD per year for 7 years compounded at 10 percent? What would be the future value it it were an annuity due?

Answer 1

Part A:

FV of Annuity = Sum [ CF * FVF(r%, n) ]

FVF (r%, n) = (1+r)^n

r = Int Rate per anum

n is no. of Years

Particulars	Amount
Cash Flow	1000
Int Rate	10.000%
Periods	7
FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
=1000 * [ [(1+0.1)^7] - 1 ] / 0.1
=1000 * [ [(1.1)^7] - 1 ] /0.1
=1000 * [ [1.9487] - 1 ] / 0.1
=1000 * [0.9487] /0.1
9487.17

Part B:

FV of Annuity Due :

= (1+r) * CF * [ (1+r)^n - 1 ] / r ]

= (1+0.10) * 1000 * [ [ (1+0.10)^7 - 1 ] /r ]

= (1.10) * 1000 * [ [ (1.10)^7 - 1 ] /0.10 ]

= (1.10) * 1000 * [ [ 1.9487 - 1 ] /0.10 ]

= (1.10) * 1000 * [ [ 0.9487 ] /0.10 ]

= USD 10,435.89