Derivation of FVA Interest Factor Formula Derivation of PVA Interest Factor Formula

0 FVA3 = a(1 + r)2 + a(1 + r)

1 + a(1 + r)

0 0 PVA3 = a(1 + r)

-1 + a(1 + r)

-2 + a(1 + r)

-3

1 FVA3 = a[(1 + r)2 + (1 + r)

1 + 1 ] 1 PVA3 = a[(1 + r)

-1 + (1 + r)

-2 + (1 + r)

-3 ]

Multiply both sides by (1 + r) . Multiply both sides by (1 + r) .

2 (1 + r) FVA3 = a[(1 + r)3 + (1 + r)

2 + (1 + r)

1 ] 2 (1 + r) PVA3 = a[(1 + r)

0 + (1 + r)

-1 + (1 + r)

-2 ]

Subtract Equation 1 from Equation 2 Subtract Equation 1 from Equation 2

3 (1 + r) FVA3 - FVA3 = a[(1 + r)3 - 1] 3 (1 + r) PVA3 - PVA3 = a[1 - (1 + r)

-3 ]

Simplify Simplify

FVA3 + r FVA3 - FVA3 = a[(1 + r)3 - 1] PVA3 + r PVA3 - PVA3 = a[1 - (1 + r)

-3 ]

Simplify Simplify

r FVA3 = a[(1 + r)3 - 1] r PVA3 = a[1 - (1 + r)

-3 ]

Simplify Simplify

4 FVA3 = a[(1 + r)3 - 1] 4 PVA3 = a[1 - (1 + r)

-3 ]

r r

FVAn = a[(1 + r)n - 1] PVAn = a[1 - (1 + r)

-n ]

r r

−

+×

I

1

I

I)(1PMT

N

++++

××××N

I)(1 I

1 -

I

1PMT