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Investment Appraisal 19 - 4
19-5 Amortization of a Loan
This calculator can be used to calculate the principal and interest portion of a
monthly installment, the remaining principal, and amount of principal and interest
repaid up to any point.
b
a
d
e
c
12 mn
a: Interest portion of installment PM1 (INT)
b: Principal portion of installment PM1 (PRN)
c: Balance of principal after installment PM2 (BAL)
d: Total principal from installment PM1 to payment of installment PM2 (ΣPRN)
e: Total interest from installment PM1 to payment of installment PM2 (ΣINT)
* a + b = one repayment (PMT)
a : INT
PM1
= I BAL
PM1–1
× i I × (PMT sign)
b : PRN
PM1
= PMT + BAL
PM1–1
× i
c : BAL
PM2
= BAL
PM2–1
+ PRN
PM2
d :
Σ
PRN = PRN
PM1
+ PRN
PM1+1
+ … + PRN
PM2
e :
Σ
INT = INT
PM1
+ INT
PM1+1
+ … + INT
PM2
PM2
PM1
PM2
PM1
BAL0 = PV (INT1 = 0 and PRN1 = PMT at beginning of installment term)
uu
uu
uConverting between the nominal interest rate and effective interest
rate
The nominal interest rate (I% value input by user) is converted to an effective
interest rate (I%') for installment loans where the number of installments per year
is different from the number of compound interest calculation periods.
I%' =
I%
(1+ ) –1
[C / Y ]
[P / Y ]
100 × [C / Y ]
{ }
×100
(Number of payments)
Amount of single payment
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