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RPN Financial 12 manual · Chapter 8 of 16

Amortization

See how each block of loan payments splits into interest and principal, and what balance is left.

8.1What amortization shows#

Each loan payment pays the interest that has built up first. The rest of the payment reduces the amount you owe. Early payments are mostly interest. Late payments are mostly principal. fAMORTn (AMORT) shows this for any block of payments.

interest=balance×iprincipal=PMT−interest\text{interest}=\text{balance}\times i \qquad \text{principal}=PMT-\text{interest}

Set up the loan (n, i, PV, PMT as usual). Key in how many payments you want to look at, then press fAMORTn. Three numbers appear on the stack.

RegisterShows
XInterest paid in those payments
YPrincipal repaid in those payments
ZThe number of payments

The amounts are shown as negative (money out). The PV register is updated to the balance after those payments, and n counts the payments made. Press AMORT again for the next block.

8.2The first year of a mortgage#

First set up the loan and calculate the payment. Then key in 12 and press AMORT.

Example 8.1

Interest and principal in year one

  1. Set up the loan and find the payment.

    360n6g12÷i200000PV0FVPMT

  2. Key in 12 and press f, AMORT.

    12fAMORTn
    After step 2: Key in 12 and press f, AMORT. The display shows: -1,199.10 / 12.00 / -2,456.01 / -11,933.19.
Result of the example "Interest and principal in year one" The display shows: -1,199.10 / 12.00 / -2,456.01 / -11,933.19.
You should seeX = −11,933.19 interest, Y = −2,456.01 principal, Z = 12.00 payments.
Example 8.2

The balance after one year

  1. Press RCL PV for the balance now owed.

    360n6g12÷i200000PV0FVPMT12fAMORTnRCLPV
Result of the example "The balance after one year" The display shows: 12.00 / -2,456.01 / -11,933.19 / 197,543.99.
You should see197,543.99
Example 8.3

Interest plus principal equals the payments made

  1. Press + to add interest and principal.

    360n6g12÷i200000PV0FVPMT12fAMORTn+
Result of the example "Interest plus principal equals the payments made" The display shows: -1,199.10 / -1,199.10 / 12.00 / -14,389.20.
You should see12 payments of 1,199.10, which is 14,389.20 (shown negative).

8.3Continue with the next block#

Press AMORT again for the next block of payments. The schedule continues from the new balance.

Example 8.4

The second year

  1. After year one, key in 12 and press f, AMORT again.

    360n6g12÷i200000PV0FVPMT12fAMORTn12fAMORTn
Result of the example "The second year" The display shows: -11,933.19 / 12.00 / -2,607.49 / -11,781.71.
You should seeLess interest and more principal than in year one.
Example 8.5

A single payment

  1. Key in 1 and press f, AMORT for the first payment alone.

    360n6g12÷i200000PV0FVPMT1fAMORTn
Result of the example "A single payment" The display shows: -1,199.10 / 1.00 / -199.10 / -1,000.00.
You should seeInterest 1,000.00 (0.5% of 200,000), principal 199.10.
Example 8.6

Start from payment number 0 to count payments

  1. Press 0 n before AMORT so n counts the payments.

    360n6g12÷i200000PV0FVPMT0n12fAMORTnRCLn
Result of the example "Start from payment number 0 to count payments" The display shows: 12.00 / -2,456.01 / -11,933.19 / 12.00.
You should see12.00

8.4Amortization with payments at the beginning#

In BEGIN mode the first payment is made at once, so it carries no interest. The first AMORT shows zero interest and the whole payment as principal.

Example 8.7

First payment in BEGIN mode

  1. BEG, 12 n, 1 i, 1000 PV, 0 FV, PMT, then 1 AMORT.

    gBEG712n1i1000PV0FVPMT1fAMORTn
Result of the example "First payment in BEGIN mode" The display shows: -87.97 / 1.00 / -87.97 / 0.00.
You should see0.00 -87.97

8.5Amortization errors#

The number of payments must be a whole number. Anything else gives Error 5.

Example 8.8

A part payment is an error

  1. Key in 1.5 and press f, AMORT.

    360n6g12÷i200000PV0FVPMT1.5fAMORTn
Result of the example "A part payment is an error" The display shows: Error 5 / 200,000.00 / 0.00 / -1,199.10 / 1.50.
You should seeError 5

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