HP 12C Financial calculator - Manual (Page 186)

186 Appendix D: Formulas Used
File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 186 of 209
Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm
Compound Interest
Without an odd period:
n
n
i FV
i
i
PMT iS PV
−
−
+ +
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡ + −
⋅ ⋅ + + = ) 1 (
) 1 ( 1
) 1 ( 0
With simple interest used for an odd period:
) ( INTG
) INTG(
) 1 (
) 1 ( 1
) 1 ( ] ) FRAC( 1 [ 0
n
n
i FV
i
i
PMT iS n i PV
−
−
+
+
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡ + −
+ + + =
With compound interest used for an odd period:
) ( INTG
) INTG(
) FRAC(
) 1 (
) 1 ( 1
) 1 ( ) 1 ( 0
n
n
n
i FV
i
i
PMT iS i PV
−
−
+
+
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡ + −
+ + + =
Amortization
n = number of payment periods to be amortized.
INT
j
= amount of PMT applied to interest in period j.
PRN
j
= amount of PMT applied to principal in period j.
PV
j
= present value (balance) of loan after payment in period j.
j = period number.
INT
1
= {0 if n = 0 and payment mode is set to Begin.
|PV
0
× i|
RND
(sign of PMT)
PRN
1
= PMT – INT
1
PV
1
= PV
0
+ PRN
1
INT
j
= |PV
j –1
× i|
RND
× (sign of PMT) for j > 1.
PRN
j
= PMT – INT
j
PV
j
= PV
j –1
+ PRN
j
∑ ∑
=
+ + + = =
n
n j
INT INT INT INT INT
1 j
2 1
...
∑ ∑
=
+ + + = =
n
n j
PRN PRN PRN PRN PRN
1 j
2 1
...
∑ + = PRN PV PV
n 0