amortize

Amortization schedule

Syntax

[Principal,Interest,Balance,Payment] = amortize(Rate,NumPeriods,PresentValue)

[Principal,Interest,Balance,Payment] = amortize(___,FutureValue,Due)

Description

[Principal,Interest,Balance,Payment] = amortize(Rate,NumPeriods,PresentValue) returns the principal and interest payments of a loan, the remaining balance of the original loan amount, and the periodic payment.

[Principal,Interest,Balance,Payment] = amortize(___,FutureValue,Due) specifies options using one or more optional arguments in addition to the input arguments in the previous syntax.

Examples

Compute an Amortization Schedule for a Conventional 30-Year, Fixed-Rate Mortgage With Fixed Monthly Payments

Compute an amortization schedule for a conventional 30-year, fixed-rate mortgage with fixed monthly payments and assume a fixed rate of 12% APR and an initial loan amount of $100,000.

Rate         = 0.12/12;   % 12 percent APR = 1 percent per month
NumPeriods   = 30*12;     % 30 years = 360 months
PresentValue = 100000;

[Principal, Interest, Balance, Payment] = amortize(Rate, ...
NumPeriods, PresentValue);

The output argument Payment contains the fixed monthly payment.

format bank

Payment

Payment = 
       1028.61

Summarize the amortization schedule graphically by plotting the current outstanding loan balance, the cumulative principal, and the interest payments over the life of the mortgage. In particular, note that total interest paid over the life of the mortgage exceeds $270,000, far in excess of the original loan amount.

plot(Balance,'b'), hold('on')
plot(cumsum(Principal),'--k')
plot(cumsum(Interest),':r')

xlabel('Payment Month')
ylabel('Dollars')
grid('on')
title('Outstanding Balance, Cumulative Principal & Interest')
legend('Outstanding Balance', 'Cumulative Principal', ... 
'Cumulative Interest')

The solid blue line represents the declining principal over the 30-year period. The dotted red line indicates the increasing cumulative interest payments. Finally, the dashed black line represents the cumulative principal payments, reaching $100,000 after 30 years.

Input Arguments

Rate — Interest-rate per period

scalar numeric decimal

Interest-rate per period, specified as a scalar numeric decimal.

Data Types: double

NumPeriods — Number of payment periods

scalar numeric

Number of payment periods, specified as a scalar numeric.

Data Types: double

PresentValue — Present value of the loan

scalar numeric

Present value of the loan, specified as a scalar numeric.

Data Types: double

FutureValue — Future value of the loan

0 (default) | scalar numeric

(Optional) Future value of the loan, specified as a scalar numeric.

Data Types: double

Due — When payments are due

0 (end of period) (default) | scalar integer with value of 0 or 1

(Optional) When payments are due, specified as a scalar integer with value of 0 (end of period) or 1 (beginning of period).

Data Types: double

Output Arguments

Principal — Principal paid in each period

vector

Principal paid in each period, returned as a 1-by-NumPeriods vector.

Interest — Interest paid in each period

vector

Interest paid in each period, returned as a 1-by-NumPeriods vector.

Balance — Remaining balance of the loan in each payment period

vector

Remaining balance of the loan in each payment period, returned as a 1-by-NumPeriods vector.

Payment — Payment per period

scalar numeric

Payment per period, returned as a scalar numeric.

More About

Amortization Schedule

An amortization schedule is a table that outlines each payment over the life of the loan, detailing the amount applied to interest and the amount applied to principal for each period.

The amortization schedule shows how the loan balance decreases over time and how much interest is paid throughout the loan term.

Version History

Introduced before R2006a