Compound Interest; Amortization - HP 12c User Manual

186 Appendix D: Formulas Used

Compound Interest

Without an odd period:
= + +
0 PV 1 ( iS
With simple interest used for an odd period:
= +
PV i
0 1 [ FRAC(
−
+ INTG
FV 1 ( i )
With compound interest used for an odd period:
= + FRAC(
0 PV 1 ( i )
−
+ INTG
FV 1 ( i )

Amortization

n = number of payment periods to be amortized.
INT = amount of PMT applied to interest in period j.
j
PRN = amount of PMT applied to principal in period j.
j
PV = present value (balance) of loan after payment in period j.
j
j = period number.
INT = {0 if n = 0 and payment mode is set to Begin.
1
|PV
PRN = PMT – INT
1
PV = PV
1
INT = |PV
j
PRN = PMT – INT
j
PV = PV
j
n
∑ ∑
=
INT INT
=
j 1
n
∑ ∑
=
PRN PRN
=
j 1
∑
= +
PV PV
n 0
File name: hp 12c_user's guide_English_HDPMBF12E44
Printered Date: 2005/7/29
⎡ − ⎤
− + n
1 1 ( i )
⋅ ⋅ +
) PMT ⎢ ⎥ FV
⎢ i ⎥
⎣ ⎦
⎡
−
1 1 (
+ +
n iS PMT ⎢
] ) 1 ( )
⎢
⎣
( n )
⎡
− +
1 1 (
n ) + +
1 ( iS ) PMT ⎢
⎢
⎣
( n )
× i| (sign of PMT)
0 RND
1
+ PRN
0 1
× i| × (sign of PMT) for j > 1.
j –1 RND
j
+ PRN
j –1 j
= + + +
INT INT ... INT
j 1 2
= + + +
PRN PRN ...
j 1
2
PRN
Page: 186 of 209
Dimension: 14.8 cm x 21 cm
−
+ n
1 ( i )
− ⎤
INTG( n )
+
i )
+
⎥
i ⎥
⎦
− ⎤
INTG( n )
i )
+
⎥
i
⎥
⎦
n
PRN
n