Mortgages Analyzed

Calculating Amortization Schedule

# What is an Amortization Schedule?

Amortization schedule shows the calculation of periodic interest and the application of periodic payment towards the principal and interest. In other words, it is a tabular presentation of the periodic payment amount, principal amount, interest, and the unpaid principal balance for each payment period. Amortization schedule is also known as an amortization table.

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# Steps in Calculating Amortization Schedule

We are taking an example of a 2 year fixed rate loan for to illustrate how an amortization schedule is calculated. The loan amount is \$100,000 and carries an interest rate of 6% per annum. The payment is made monthly and interest is compounded monthly. The steps are described in detail below.

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## Step 1: Calculate Periodic Payment

The first step is to calculate periodic payment.

Where,

 P = principal amount = \$100,000 r = annual interest rate = 6% t = time in years/loan term = 2 c = compounding periods per year = 12 (monthly compounding) i = periodic interest rate (r/c) = 6%/12 = 0.005 n = number of periods = t × c = 2 × 12 = 24

Given the information above, we can calculate the payment using the formula below.

PMT = periodic payment = [ P × i × (1+i)n ] [ (1+i)n – 1 ] = [ 100,000 × 0.005 × (1+0.005)24 ] [ (1+0.005)24 – 1 ] = \$4,432.06

The payment remains the same each month. The amortization schedule will show how the monthly payment pays off the entire principal loan amount and interest at the end of the loan period.

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## Step 2: Calculate Starting Balance

For the first period the starting balance is the principal balance. For all subsequent periods the initial balance is the ending balance/unpaid principal balance of previous period.

In our example,

Period 1: starting balance is \$100,000.

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## Step 3: Calculate Periodic Interest

Periodic interest = starting balance × periodic interest rate

In period 1:
 Periodic interest = \$100,000.00 × 0.005 = \$500.00
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## Step 4: Calculate New Balance

New balance is the sum of starting amount and periodic interest.

In period 1:
 Periodic interest = \$100,000.00 + \$500.00 = \$100,500.00

The new balance reflects the amount that would be required to pay the entire loan balance.

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## Step 5: Apply Payment and Calculate Ending Balance

Ending balance = new balance – payment amount

In period 1:
 Ending balance = \$100,500.00 - \$4,432.06 = 96,067.94

Ending balance is generally known as unpaid principal balance (UPB).

Optionally you can also calculate the principal reduction amount, which is the amount of principal that was paid in the period.

Principal reduction amount = Payment/PMT – periodic interest

In period 1:
 Principal reduction amount = \$4,432.06 - \$500.00 = \$3,932.06
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## Step 6: Repeat Steps 2 to 5 for Subsequent Periods

Repeat steps 2 to 5 for each period to calculate the amortization schedule.

For period 2:
 • Starting balance is the ending balance/UPB for period 1, which is \$96,067.94
 • Periodic interest = \$96,067.94 × 0.005 = \$480.34
 • New balance = \$96,067.94 + \$480.34 = \$96,548.28
 • Ending balance = \$96,548.28 - \$4,432.06 = \$92,116.22
 • Principal reduction amount = \$4,432.06 - \$480.34 = \$3,951.72
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For period 24:
 • Starting balance = \$4,410.01
 • Periodic interest = \$4,410.01 × 0.005 = \$22.05
 • New balance = \$4,410.01 + \$22.05 = \$4,432.06
 • Ending balance = \$4,432.06 - \$4,432.06 = \$0.00
 • Principal reduction amount = \$4,432.06 - \$22.05 = \$4,410.01

The complete amortization schedule is presented below.

### Loan Parameters

\$4,432.06
\$6369.48
Monthly Payment
Total Interest Paid
\$106,369.44
24 Months
Total Payments
Period
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### Amortization Schedule

Period

Starting
Balance
Interest

New
Balance
Periodic
Payment
Principal
Reduction
Unpaid
Balance
1 \$100,000.00 \$500.00 \$100,500.00 \$4,432.06 \$3,932.06 \$96,067.94
2 \$96,067.94 \$480.34 \$96,548.28 \$4,432.06 \$3,951.72 \$92,116.22
3 \$92,116.22 \$460.58 \$92,576.80 \$4,432.06 \$3,971.48 \$88,144.74
4 \$88,144.74 \$440.72 \$88,585.46 \$4,432.06 \$3,991.34 \$84,153.40
5 \$84,153.40 \$420.77 \$84,574.17 \$4,432.06 \$4,011.29 \$80,142.11
6 \$80,142.11 \$400.71 \$80,542.82 \$4,432.06 \$4,031.35 \$76,110.76
7 \$76,110.76 \$380.55 \$76,491.31 \$4,432.06 \$4,051.51 \$72,059.25
8 \$72,059.25 \$360.30 \$72,419.54 \$4,432.06 \$4,071.76 \$67,987.48
9 \$67,987.48 \$339.94 \$68,327.42 \$4,432.06 \$4,092.12 \$63,895.36
10 \$63,895.36 \$319.48 \$64,214.84 \$4,432.06 \$4,112.58 \$59,782.78
11 \$59,782.78 \$298.91 \$60,081.69 \$4,432.06 \$4,133.15 \$55,649.63
12 \$55,649.63 \$278.25 \$55,927.88 \$4,432.06 \$4,153.81 \$51,495.82
13 \$51,495.82 \$257.48 \$51,753.30 \$4,432.06 \$4,174.58 \$47,321.23
14 \$47,321.23 \$236.61 \$47,557.84 \$4,432.06 \$4,195.45 \$43,125.78
15 \$43,125.78 \$215.63 \$43,341.41 \$4,432.06 \$4,216.43 \$38,909.35
16 \$38,909.35 \$194.55 \$39,103.89 \$4,432.06 \$4,237.51 \$34,671.83
17 \$34,671.83 \$173.36 \$34,845.19 \$4,432.06 \$4,258.70 \$30,413.13
18 \$30,413.13 \$152.07 \$30,565.20 \$4,432.06 \$4,280.00 \$26,133.14
19 \$26,133.14 \$130.67 \$26,263.80 \$4,432.06 \$4,301.40 \$21,831.74
20 21,831.74 \$109.16 \$21,940.90 \$4,432.06 \$4,322.90 \$17,508.84
21 \$17,508.84 \$87.54 \$17,596.38 \$4,432.06 \$4,344.52 \$13,164.32
22 \$13,164.32 \$65.82 \$13,230.14 \$4,432.06 \$4,366.24 \$8,798.08
23 \$8,798.08 \$43.99 \$8,842.07 \$4,432.06 \$4,388.07 \$4,410.01
24 \$4,410.01 \$22.05 \$4,432.06 \$4,432.06 \$4,410.01 \$0.00
Source :www.MortgagesAnalyzed.com

Source :www.MortgagesAnalyzed.com

Updated: Jan 12, 2017

Learn how to build the amortization schedule for your mortgage loan.
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