Amortization

Amortize means to put money aside at regular intervals for the gradual repayment of a debt. The lender charges interest at a fixed rate on the unpaid portion of the debt.

Payment size

The payment size PS needed to amortize a loan of P dollars is

          P i
PS =              
     1 - (1 + i)^-n

where

PS = payment size
P = principal (loan amount)
r = annual interest rate (a.p.r.)
m = number of payments per year also the number of compounding periods per year
t = time in years
     r
i =     = interest rate per compounding period
     m
n = m t = total number payments

Amortization tables

An amortization table consists of the following columns.
period :: payment size :: interest :: payment towards principle :: outstanding principal

Example: A loan of $50,000 is to be repaid over a five year period with equal
payments made at the end of each year. If an annual interest rate of
8% is charged on the unpaid balance, calculute the payment size and
create an amortization table.

i = 0.08/1 = 0.08
n = 5
PS = P i/(1 - (1 + i)^-n) = 50,000(0.08)/(1 - (1 + 0.08)^-5) = $12,522.82

Period	Payment	Interest	Payment to principal	Outstanding principle
0	0	0	0	50000.00
1	12522.82	4000.00	8522.82	41477.18
2	12522.82	3318.17	9204.65	32272.53
3	12522.82	2581.80	9941.02	22331.51
4	12522.82	1786.52	10736.30	11595.21
5	12522.82	927.62	11595.21	0

Exercises


(1) A family financed a home costing $150,000.  They made a down
    payment of $15,000 and secured a mortage with an interest rate
    of 8.5% per year on the unpaid balance.  If the loan is to be
    repaid over a 30 year period, calculate the size of the monthly
    payment.
     $1,038.03
     $1,153.37
     $106,250.00


(2) Compute the amount of equity the previous family will have in 
    the home after 20 years.
     $51,278.24
     $56,975.55
     $66,278.24

Calculator

If you do not mind waiting a few seconds press the following button to generate an amortization table. The amortization table shows how each payment is broken down into payment towards interest and payment towards the principal.

Principal
Annual interest rate as a decimal
Number of payments per year
Length of the loan years