HP HP12C hp 12c_user's guide_English_E_HDPMBF12E44.pdf - Page 186

Appendix D: Formulas Used

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186 Appendix D: Formulas Used Compound Interest Without an odd period: 0 = PV + (1+ iS) ⋅ PMT ⋅ ⎡1− (1+ i)−n ⎢ ⎢⎣ i + FV (1+ i)−n With simple interest used for an odd period: 0 = PV [1+ iFRAC(n)] + (1+ iS)PMT ⎡1 (1+ i ) − INTG(n) i + FV (1+ i)−INTG(n) With compound interest used for an odd period: 0 = PV (1+ i)FRAC(n) + (1+ iS)PMT ⎡1 (1+ i ) − INTG(n) i + FV (1+ i)−INTG(n) Amortization n INTj PRNj PVj = number of payment periods to be amortized. = amount of PMT applied to interest in period j. = amount of PMT applied to principal in period j. = present value (balance) of loan after payment in period j. j INT1 PRN1 PV1 INTj PRNj PVj = period number. = {0 if n = 0 and payment mode is set to Begin. |PV0 × i|RND (sign of PMT) = PMT - INT1 = PV0 + PRN1 = |PVj -1 × i|RND × (sign of PMT) for j > 1. = PMT - INTj = PVj -1 + PRNj n ∑ INT = ∑ INTj = INT1 + INT2 + ... + INTn j=1 n ∑ PRN = ∑ PRNj = PRN1 + PRN2 + ... + PRNn j=1 PVn = PV0 + ∑ PRN File name: hp 12c_user's guide_English_HDPMBF12E44 Printered Date: 2005/7/29 Page: 186 of 209 Dimension: 14.8 cm x 21 cm

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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