# Amortization schedule

An amortization schedule is a table detailing each periodic payment on an amortizing loan (typically a mortgage), as generated by an amortization calculator. Amortization refers to the process of paying off a debt (often from a loan or mortgage) over time through regular payments. A portion of each payment is for interest while the remaining amount is applied towards the principal balance. The percentage of interest versus principal in each payment is determined in an amortization schedule. The schedule differentiates out the portion of payment that belongs to interest expense and the portion used to close the gap of a discount or premium from the principal after each payment.

While a portion of every payment is applied towards both the interest and the principal balance of the loan, the exact amount applied to principal each time varies (with the remainder going to interest). An amortization schedule reveals the specific monetary amount put towards interest, as well as the specific amount put towards the principal balance, with each payment. Initially, a large portion of each payment is devoted to interest. As the loan matures, larger portions go towards paying down the principal.

## Methods of amortization

There are different methods in which to arrive at an amortization schedule. These include:

• Straight line (linear)
• Declining balance
• Annuity
• Bullet (all at once)
• Balloon (amortization payments and large end payment)
• Increasing balance (negative amortization)

Amortization schedules run in chronological order. The first payment is assumed to take place one full payment period after the loan was taken out, not on the first day (the amortization date) of the loan. The last payment completely pays off the remainder of the loan. Often, the last payment will be a slightly different amount than all earlier payments.

In addition to breaking down each payment into interest and principal portions, an amortization schedule also reveals interest-paid-to-date, principal-paid-to-date, and the remaining principal balance on each payment date.

## Amortization schedule assumptions

This amortization schedule is based on the following assumptions:

First, it should be known that rounding errors occur and depending how the lender accumulates these errors, the blended payment (principal + interest) may vary slightly some months to keep these errors from accumulating; or, the accumulated errors are adjusted for at the end of each year, or at the final loan payment.

There are a few crucial points worth noting when mortgaging a home with an amortized loan. First, there is substantial disparate allocation of the monthly payments toward the interest, especially during the first 18 years of a 30 year mortgage. In the example below, payment 1 allocates about 80-90% of the total payment towards interest and only \$67.09 (or 10-20%) toward the Principal balance. The exact percentage allocated towards payment of the principal depends on the interest rate. Not until payment 257 or over two thirds through the term does the payment allocation towards principal and interest even out and subsequently tip the majority toward the former.

For a fully amortizing loan, with a fixed i.e. non-variable interest rate, the payment remains the same throughout the term, regardless of principal balance owed. For example, the payment on the above scenario will remain \$733.76 regardless if the principal balance is \$100,000 or \$50,000. Paying down more than the monthly contractual amount reduces the amount outstanding and thus the interest that payable to the lender: if the monthly payment stays the same, the number of payments and the term of the loan must reduce. Conversely, paying down less than the monthly contractual amount increases the amount outstanding and thus the interest payable: if the monthly payment stays the same, the number of payments and the term of the loan must increase.

## Outstanding loan balance calculation

The outstanding loan balance at any given time during the term of a loan can be calculated by finding the present value of the remaining payments at the given interest rate. This amount will consist of principal only.

Example of O/S loan balance calculation:

• Loan *Term=*Interest Rate = 3%
• Payment is monthly

Question: What is the loan balance at the end of year?

First, calculate the monthly payments by using the loan amount (\$12,842.74 as present value, term as 13 weeks, interest at 3%). This will give you a monthly payment of \$1000.00. The Present Value of an Annuity formula should be used here to solve for monthly payment.

Next, in order to find the outstanding loan balance you will need to find the present value of the remaining payments. Use the monthly payment of \$775.30 as the payment function, the term will be 156 ((20-7)x12), and .583333% as the rate. This will give you an outstanding loan balance of \$79,268.02. Again, the Present Value of an Annuity formula should be used.

This means that at the end of year seven the loan can be paid off in full for the amount of \$79,268.02. Typically mortgage lenders will have a balloon payment clause in the contract that will charge a fee for early payment. This is because the lender will not get the same yield if loan balance is not held to maturity.

Similarly here is a table that shows both the interest and principal portions paid for the first two years.

Period Interest Principal Balance
1 \$583.33 \$191.97 \$99,808.03
2 \$582.21 \$193.09 \$99,614.95
3 \$581.09 \$194.21 \$99,420.74
4 \$579.95 \$195.34 \$99,225.39
5 \$578.81 \$196.48 \$99,028.91
6 \$577.67 \$197.63 \$98,831.28
7 \$576.52 \$198.78 \$98,632.50
8 \$575.36 \$199.94 \$98,432.55
9 \$574.19 \$201.11 \$98,231.44
10 \$573.02 \$202.28 \$98,029.16
11 \$571.84 \$203.46 \$97,825.70
12 \$570.65 \$204.65 \$97,621.05
13 \$569.46 \$205.84 \$97,415.21
14 \$568.26 \$207.04 \$97,208.16
15 \$567.05 \$208.25 \$96,999.91
16 \$565.83 \$209.47 \$96,790.45
17 \$564.61 \$210.69 \$96,579.76
18 \$563.38 \$211.92 \$96,367.84
19 \$562.15 \$213.15 \$96,154.69
20 \$560.90 \$214.40 \$95,940.29
21 \$559.65 \$215.65 \$95,724.64
22 \$558.39 \$216.91 \$95,507.74
23 \$557.13 \$218.17 \$95,289.57
24 \$555.86 \$219.44 \$95,070.13