HP 12C - Compound Interest; Amortization

Appendix E: Formulas Used 251
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 251 of 275
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm
Compound Interest
Without an odd period:
n
n
iFV
i
i
PMTiSPV
−
−
++
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+−
⋅⋅++= )1(
)1(1
)1(0
With simple interest used for an odd period:
)(INTG
)INTG(
)1(
)1(1
)1(])FRAC(1[0
n
n
iFV
i
i
PMTiSniPV
−
−
+
+
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+−
+++=
With compound interest used for an odd period:
)(INTG
)INTG(
)FRAC(
)1(
)1(1
)1()1(0
n
n
n
iFV
i
i
PMTiSiPV
−
−
+
+
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+−
+++=
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
nj
INTINTINTINTINT
1j
2
1
...
∑∑
=
+++==
n
nj
PRNPRNPRNPRNPRN
1j
2
1
...
∑
+= PRNPVPV
n
0