Loan Amortisation

Loan amortisation describes the way in which the principal of the loan reduces over time.

When a borrower makes a monthly payment, some of the money is used to pay interest on the loan. The rest of the payment is used to repay the principal.

For example, we can Ccnstruct an amortization schedule for a $1,000, 10% annual rate loan with 3 equal payments. The loan payment $P M T$ can be found using the present value of annuity formula:

P M T = \frac{P V A}{\frac{1}{r} - \frac{1}{r \cdot (1 + r)^{T}}} = \frac{1, 000}{\frac{1}{0.1} - \frac{1}{0.1 \times (1 + 0.1)^{3}}} \approx $ 402.11

The loan amortisation table:

Year	Beg Bal	PMT	Int	Prin	End Bal
1	$1,000	$402	$100	$302	$698
2	698	402	70	332	366
3	366	402	36	366	0
	Total	1,206	206	1,000