Question 3: How do you make an amortization table?
An amortization table (also called an amortization schedule) records the portion of the
payment that applies to the principal and the portion that applies to interest. Using this
information, we can determine exactly how much is owed on the loan at the end of any
period.
Amortization tables are useful when a loan is to be paid off. Recall that when we
calculated the payment, we rounded the amount of the payment up to the penny. Over
the term of the loan, we might pay an additional amount each month leading to the
principal being reduced more quickly than anticipated. When the final loan payment is
made, it needs to be adjusted to insure the balance is paid off properly. Different
lenders round payments and interest differently. This may lead to slightly different
numbers in the amortization table.
Suppose you want to borrow $10,000 for an automobile. Navy Federal Credit Union
offers a loan at an annual rate of 1.79% amortized over 12 months. The payment would
be
PMT 
0.0179
12
10000
1  1  0.0179
12 
12
 841.44
Since payments are made to the penny, a payment of $841.44 would lead to an
overpayment of almost a half of a penny. While this may not seem like much, over the
term of the loan it can add up. Financial institutions need to accurately account for these
small amounts to insure their books are balanced. An amortization table helps them to
do this.
Amortization tables generally have five columns. These columns track the payment
number, the amount of the payment, the interest paid in the payment, the portion of the
payment applied to the balance, and the outstanding balance on the loan after the
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payment is made. Let’s look at how the amounts in the table are calculated. We’ll do
this by looking at the different rows of the table, one at a time.
Payment
Number
Amount of
Payment
Interest in the
Payment
Amount in
Payment Applied
to Balance
Outstanding
Balance at the
End of the Period
0
$10,000
The first row of the table helps us to establish the initial balance on the loan. We call it
payment 0 since it does not correspond to an actual payment. Using this balance, we
can determine the portion of the payment, $841.44, that is applied to the balance and
the portion that is interest.
Payment
Number
Amount of
Payment
Interest in the
Payment
Amount in
Payment Applied
to Balance
Outstanding
Balance at the
End of the Period
0
1
$10,000
$841.44
$14.92
$826.52
$9173.48
The interest in the payment is calculate by multiplying the interest rate per period times
the balance at the end of the previous period,
Interest in Payment 1 
0.0179
12
 $10, 000
 $14.92
In this amortization table, we will round interest amounts to the nearest penny. In
practice, you should check with the lender to see how they round interest in the table.
Since the amount applied to balance is the difference between the payment and the
interest,
Amount in Payment 1 Applied to Balance  $841.44  $14.92
 $826.52
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This amount reduces the balance at the end of the period,
Balance at the End of the First Period  $10, 000  $826.52
 $9173.48
This strategy is also used to fill in the amounts for the second payment. However, in this
case, the interest is calculated using the balance after the previous period.
Payment
Number
Amount of
Payment
Interest in the
Payment
Amount in
Payment Applied
to Balance
0
Outstanding
Balance at the
End of the Period
$10,000
1
$841.44
$14.92
$826.52
$9173.48
2
$841.44
$13.68
$827.76
$8345.72
0.0179
12
 9173.48
841.44  13.68
9173.48  827.76
As the balance decreases, the interest also decreases. This means that a larger and
larger portion of the payment goes to paying off the balance.
Payments 3 through 11 are carried out in a similar fashion to give the next few rows.
Remember, in this table we are rounding interest amounts to the nearest penny.
Payment
Number
Amount of
Payment
Interest in the
Payment
Amount in
Payment Applied
to Balance
0
Outstanding
Balance at the
End of the Period
$10,000
1
$841.44
$14.92
$826.52
$9173.48
2
$841.44
$13.68
$827.76
$8345.72
3
$841.44
$12.45
$828.99
$7516.73
4
$841.44
$11.21
$830.23
$6686.50
5
$841.44
$9.97
$831.47
$5855.03
6
$841.44
$8.73
$832.71
$5022.32
7
$841.44
$7.49
$833.95
$4188.37
13
8
$841.44
$6.25
$835.19
$3353.18
9
$841.44
$5.00
$836.44
$2516.74
10
$841.44
$3.75
$837.69
$1679.05
11
$841.44
$2.50
$838.94
$840.11
For the last payment, we need to pay off the outstanding balance of $840.11. This
means the amount of the last payment applied to the balance must be $840.11. The
interest in the last payment is
Interest in Payment 12 
0.0179
12
 $840.11
 $1.25
Combining these two amounts gives the amount of the last payment,
Amount of Payment 12  $840.11  1.25
 $841.36
With these amounts, we can complete the amortization table.
Payment
Number
Amount of
Payment
Interest in the
Payment
Amount in
Payment Applied
to Balance
0
Outstanding
Balance at the
End of the Period
$10,000
1
$841.44
$14.92
$826.52
$9173.48
2
$841.44
$13.68
$827.76
$8345.72
3
$841.44
$12.45
$828.99
$7516.73
4
$841.44
$11.21
$830.23
$6686.50
5
$841.44
$9.97
$831.47
$5855.03
6
$841.44
$8.73
$832.71
$5022.32
7
$841.44
$7.49
$833.95
$4188.37
8
$841.44
$6.25
$835.19
$3353.18
9
$841.44
$5.00
$836.44
$2516.74
14
10
$841.44
$3.75
$837.69
$1679.05
11
$841.44
$2.50
$838.94
$840.11
12
$841.36
$1.25
$840.11
$0
If we add the interest amounts, we find the total amount of interest paid is $97.20.
If we round the payment or interest amounts differently, the amortization table yields
different amounts of interest. In the next example, we round all payments and interest
amounts up to the nearest penny to see how these change the total amount of interest
paid.
Example 4
Make an Amortization Table
Suppose Navy Federal Credit Union rounds all interest and payment
amounts up.
a. Find the amortization table on a loan of $10,000 amortized at an
annual rate of 1.79% over 12 months with monthly payments.
Solution The terms of the loan are the same as was described above. If
the payment is rounded up, we still get a payment of $841.44. When we
carry out the process described earlier, we get the table below.
Payment
Number
Amount of
Payment
Interest in the
Payment
Amount in
Payment Applied
to Balance
0
Outstanding
Balance at the
End of the Period
$10,000
1
$841.44
$14.92
$826.52
$9173.48
2
$841.44
$13.69
$827.75
$8345.73
3
$841.44
$12.45
$828.99
$7516.74
4
$841.44
$11.22
$830.22
$6686.52
5
$841.44
$9.98
$831.46
$5855.06
6
$841.44
$8.74
$832.70
$5022.36
15
7
$841.44
$7.50
$833.94
$4188.42
8
$841.44
$6.25
$835.19
$3353.23
9
$841.44
$5.01
$836.43
$2516.80
10
$841.44
$3.76
$837.68
$1679.12
11
$841.44
$2.51
$838.93
$840.19
12
$841.45
$1.26
$840.19
$0
In this table, several of the payments include a slightly higher amount of
interest. This means that less of the payment goes towards the
outstanding balance. This amount is made up in the last payment where
$840.19 is paid to bring the balance to zero. This causes the final
payment to be slightly higher.
b. Add the interest amount in the third column to find the total amount
of interest paid.
Solution The sum of the interest amounts is $97.29. This is slightly
higher than when interest amounts are rounded to the nearest penny.
This is to be expected since we rounded all interest amounts up.
The payments and interest amounts may be rounded to the nearest penny, rounded up
to the nearest penny, or rounded down to the nearest penny. In all cases, any
discrepancies are made up in the final payment.
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