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
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