Amortization Tables

1
Amortization Tables

• Section 5.4

2
Amortization

• Amortization is the process of paying of a large
  sum by equal, periodic payments.
• Each payment will consist of interest owed on the
  loan and repayment of the principal.
• The interest is computed by finding the periodic
  interest owed on the balance from the beginning
  of the period.
• The new balance is then computed by subtracting
  the payment on the principal.

3
Amoritization, example

• Find the principal and interest in the first
  three monthly payments on a 150,000 loan over 30
  years with annual interest rate of 6.45
  compounded monthly.
• We need to begin by finding the monthly payment.
  Since this is essentially an (ordinary) annuity,
  we can use the formula
• We have A 150,000, n 30(12), and r
  .0645/12
• So the monthly payments will be 943.18.

4

• Now we need to find how much of each payment will
  be applied to interest and how much can be
  applied to the balance.
• At the end of the first month, we owe
  150,000(.005375) 806.25.
• So 806.25 is used to pay the interest and the
  remainder (136.93) is used to reduce the
  balance. So at the beginning of the second month
  the balance is 149,863.07.
• At the end of the second month we owe
  149,863.07(.005375) 805.52 in interest, and
  137.66 is paid on the principal.
• So at the beginning of the third month the
  balance owed is 149,725.41
• So we compute the interest for the third month,
  149,725.41(.005375) 804.78
• So we pay this, 138.40 on the principal, and are
  left with a balance of 149,587.01

5
Amortization schedule

• To make all this easier, we can arrange all the
  necessary information in a table, called an
  amortization schedule.
• For each period we need to include the number of
  the payment period, the balance at the beginning,
  the interest due, the payment amount, and the
  amount applied to the principal.
• The payment amount is computed using the annuity
  formula, and once we know the balance due at the
  beginning of a period, we can compute the
  interest and principal paid that period, and thus
  the balance for the next period.

6
Amortization schedule, example

• Lets find the amortization schedule for a
  25,000 loan at 8 interest compounded annually
  to be repaid in five yearly payments.
• First we need to find the payment amount,
• So the yearly payments will be 6261.41.
• Now we are ready to start the schedule.

7

• We start with the 25,000 initial balance and
  compute the interest and principal paid in the
  first payment.

2000
4261.41
1659.09
6261.41
4602.32
20,738.59
1290.90
4970.51
16,136.27
6261.41
6261.41
893.26
5368.15
11,165.76
6261.42
463.81
5797.61
5797.61
At the end we owe more than the 6261.41 payment.
Why?
8
Amortization schedule, example

• Find the amortization schedule for a 3000 loan
  to be paid off in 2 years with quarterly
  payments. The interest on the loan is 7.5
  annual interest compounded quarterly.
• So the quarterly payment is 407.33

9
351.08

• 56.25

49.67
407.33
357.66
2648.92
364.37
2291.26
42.96
407.33
1926.89
407.33
36.13
371.20
1555.69
29.17
407.33
378.16
1177.53
22.08
407.33
385.25
14.86
407.33
792.28
392.47
399.81
7.50
407.31
399.81
10
Key Suggested Problems

• Sec. 5.4 7, 8, 9, 10, 11, 19, 20, 21