Amortizing a Loan

Amortizing a Loan                   

It is the repayment of interest and principle to put off a loan by maturity.

The distinguish feature of this loan is that it is repaid in equal periodic payments that include both interest and principal.

For Example, suppose you borrow 10000 dollars at 10 percent compounded annual interest to be repaid over the next 5 years. So we need to find equal installment payments at the end of each year for amortization.

So the equation becomes

$10000 = R (PVIFA10%,5)

Where R= Annual Interest Payment

PVIFA = Present value of interest factor of Annuity

$10000 = R [1 – {1/ (1 + i) power n}/i]

$10000 = R [1 – {1/ (1 + 0.10) power 5}/0.10]

$10000 = R (3.791)

R= $2638

(1) End of Year	(2) Installment Payment	(3) Annual Interest $ (5)*10%	(4) Principal Payment (2)-(3)	(5) Principal Amount Owing At Year End (5)previous amount-(4)
0	$2638	-	-	$10000
1	2638	$1000	$1638	8362
2	2638	836	1802	6560
3	2638	656	1982	4578
4	2638	458	2180	2398
5	2638	239	2398	-

Here we have learnt that as the time passes by, the proportion composed of Principal Payment increases while the proportion composed of Annual Interest decreases.