15-5-4

Amortization

Calculation Formulas

a

 

 

 

e

 

 

 

 

 

1 payment

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 payment

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

d

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

PM1.....................

PM2 ............

 

Last

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1...............

 

 

 

 

PM1..................

 

 

 

PM2 ...............

Last

 

 

 

 

 

 

Number of Payments

 

 

 

 

 

 

 

 

 

 

Number of Payments

 

 

a: Interest portion of payment PM1 (INT) INTPM1 = I BALPM1–1σ i I σ (PMT sign)

b: Principal portion of payment PM1 (PRN) PRNPM1 = PMT + BALPM1–1σ i

c: Principal balance upon completion of payment PM2 (BAL)

BALPM2 = BALPM2–1 + PRNPM2

d: Total principal paid from payment PM1 to payment PM2 (3PRN)

PM2

3 PRN = PRNPM1 + PRNPM1+1 + .... + PRNPM2

PM1

e: Total interest paid from payment PM1 to payment PM2 (3INT)

a + b = one repayment (PMT)

PM2

 

INT = INTPM1 + INTPM1+1 + .... + INTPM2

PM1

 

BAL0 = PV .......................

Payment: End (Format tab)

INT1 = 0, PRN1 = PMT ... Payment: Begin (Format tab)

Converting 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 annual payments is different from the number of annual compoundings calculation periods.

I%' = {(1+

I%

 

[C / Y ]

 

}100

)[P / Y ]–1

100 ⋅ [C / Y ]

The following calculation is performed after conversion from the nominal interest rate to the effective interest rate, and the result is used for all subsequent calculations.

i = I%'100

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