Amortization Schedule

Study guide: Exam FM-2

An amortization schedule is a table that breaks every loan payment into its interest and principal components, and tracks the Outstanding Balance over the life of the loan. For a level-payment loan with payment $P$ , interest rate $i$ , and $n$ periods, each row contains:

Column	Formula
Payment number $k$	$1, 2, \ldots, n$
Payment amount	$P$ (constant)
Interest portion $I_k$	$OB_{k-1} \times i$
Principal portion $PR_k$	$P - I_k$
Outstanding balance $OB_k$	$OB_{k-1} - PR_k$

The principal portions form a geometric sequence: $PR_k = PR_1 \cdot (1+i)^{k-1}$ . The schedule ends when $OB_n = 0$ .

3-Payment Amortization Schedule A $ $3{,}000$ loan is repaid with 3 level annual payments at $i = 10\%$ . Construct the full amortization schedule.

Answer Payment: $P = 3000 / a_{\overline{3}|10\%} = 3000 / 2.4869 = \$1{,}206.34$

Period Payment Interest Principal Balance

0 — — — $3{,}000.00$

1 $1{,}206.34$ $300.00$ $906.34$ $2{,}093.66$

2 $1{,}206.34$ $209.37$ $996.97$ $1{,}096.69$

3 $1{,}206.34$ $109.67$ $1{,}096.67$ $\approx 0$

The interest column decreases each period (charged on a smaller balance), while the principal column increases. The small rounding discrepancy in period 3 disappears with exact arithmetic.

Period	Payment	Interest	Principal	Balance
0	—	—	—	$3{,}000.00$
1	$1{,}206.34$	$300.00$	$906.34$	$2{,}093.66$
2	$1{,}206.34$	$209.37$	$996.97$	$1{,}096.69$
3	$1{,}206.34$	$109.67$	$1{,}096.67$	$\approx 0$