## Instructions

The calculator is split into three sections:

1. Sliders

2. Graphs & tables

3. Input boxes

### 1. Sliders

Move the sliders to set the values of your principal, interest rate, loan length, and mortgage start date.

Up and down arrows at either side of the slider allow the range of values covered by the slider to be adjusted.

The checkboxes on the left of the sliders determine whether principal, interest, term or payment is calculated. By default, the Payment slider checkbox is ticked, meaning that moving the other sliders' values will calculate the payment. Clicking on another slider checkbox, e.g. Principal checkbox, allows the user to modify term, interest and payment to see the Principal value calculated as these other values change.

### 2. Graphs & tables

Use the buttons underneath the graphs and tables to choose how you want the output to be displayed:

• Amortization Graph - this shows how the monthly payments made each year are broken down. Note how the curves show increased principal and decreased interest being paid as time goes by. Also note that extra payments "push" up the principal curve, i.e. the annual principal amount shown is increased by the value of the extra payment.

• Repayment Chart - the percentage breakdown of the total payments made over the entire mortgage (or indeed, the breakdown of the average monthly payment).

• Balance Graph - this shows the balance outstanding over the term of the mortgage. It is useful when extra payments are made to visually see how much sooner the mortgage is paid off, and how quickly the balance drops.

• Interest Graph - this shows the rate of interest used over the term of the mortgage.

• Annual Amortization Table - how much interest and principal you pay each year.

• Monthly Amortization Table - how much interest and principal you pay each year, broken down month by month.

• Monthly Payments Table - the payment amount and any extra payment made each month. Useful when interest rates change or if extra payments reduce monthly payment.

• Summary - shows a summary of the current values.

• Settings:

• Payment frequency - most mortgages are paid monthly. If you change the payment frequency, you should probably change the compound period to match the payment frequency (exceptions are Canadian and some UK mortgages). Accelerated bi-weekly makes a payment every two weeks so you end up with 26 payments a year - the equivalent of 13 monthly payments in a year - the extra payments shorten the term.

• Compound period - monthly is the standard compound period for amortization. This matches monthly payments. In Canada, payment frequency can be monthly but semi-annual compounding is used. In the UK, payments can be made monthly, but some Building Societies still use an annual rest system whereby interest is calculated once per year and the monthly payment is one twelfth of the annual payment due.

• Rounding: no rounding means that full values are stored internally and rounding is only used when displaying values. Rounding means that every value stored internally is rounded to two decimal places using the selected rounding method. These internal values will match the displayed value. In this case, the final payment may be increased to compensate for rounding errors over the life of the loan.

• PMI - Switch it off, choose your FICO rating for automatic calculation, or manually enter the percentage to be applied

• Year number - You can choose to show the calendar year or the year number in the graphs and tables.

• Extra payments - default is to reduce term when extra payments are made, but alternative is to keep term unchanged and reduce monthly payment instead.

• Interest sliders - You can use either 1/8th increments or decimal places.

• Initial Payment Date - Beginning of period uses the first day of the next month. End of period uses the first day of the month after the next month. End of period is the default for most mortgages.

• Dynamic / static - Dynamic calculation means that calculations are done as you move the slider; this is the default. Static means that the calculations are done when you've finished dragging the slider.

### 3. Input boxes

The bottom of the calculator is split in two:

• Fixed Loan Data

1. Expenses (USA-only)

2. Prepayments

3. Extra payments

4. Interest rates

5. ARM (USA-only)

The Fixed Loan Data section stays constant while the other five sections can be chosen using the buttons at the bottom of the calculator.

Fixed Loan Data - use this as an alternative to the sliders for entering values. This section is called fixed because it does not take interest rate changes into account. The total interest paid over the entire mortgage is shown on the right hand side along with the total interest paid as a percentage of all payments made (see the Repayment Chart for a graphical view). The total payments figure includes principal and interest but not any other mortgage-related expenses.

The five optional sections:

1. Expenses - On the left hand side, you can enter monthly HOA and two other monthly expenses. The annual Tax and Insurance fields are simply divided by 12 and added to the periodic payment amount. The PMI percentage can be entered if manual PMI mode is selected in the Settings, otherwise the PMI status is displayed. On the right hand side, the expenses figure is a total of all monthly and annual expenses for the given period. When this is added to the PMI due, a total payment for the period is shown. Overall figures for insurance, tax and PMI for the duration of the mortgage are also shown.

2. Prepayment Data - this section gives you the opportunity to estimate how you can shorten the term of your mortgage by making either a single one-off payment or continuous extra monthly or annual payments. You must enter a starting month for the prepayment to take effect. The format is simply the month number i.e. 1 for the first month, 2 for the second month and so on. On the right-hand side, the Savings field shows you how much money you will save given amount of extra payments maid. The dates shown reflect what happens to the mortgage term when the extra payments have been factored in.

3. Extra payments - add up to six extra one-time payments, giving the start and end months numbers to indicate the period when the extra payment is to be made.

4. Interest rates - add up to five extra interest rates, giving the start and end month numbers to indicate when the interest rate is active. Months outside these ranges will use the fixed loan data interest rate. To specify a period where no principal is paid, enter a start and end month in the interest-only payments section.

5. ARM - Adjustable Rate Mortgage support is provided in this section. Enter a start month to activate and click on the interest rate graph to view how this section alters the interest rates over the term of the mortgage.

## Notes

Enter the nominal interest rate not an APR.
All calculations are performed on a monthly basis.
The figures are estimates only - your lender's figures will vary!

## Amortization formula

Karl's Mortgage Calculator uses a standard amortization formula commonly used around the world. Interest is calculated on a monthly basis. Most financial institutions base their calculations on this formula, but many will calculate interest on a daily, weekly or even annual basis. The figures generated by the calculator should therefore approximate what your lender will charge you, but you should always contact your lender for exact details on how and when they charge interest on outstanding principal balances.

The text below is from Hugh Chou's web site.

First you must define some variables to make it easier to set up:

• P = principal, the initial amount of the loan

• I = the annual interest rate (from 1 to 100 percent)

• L = length, the length (in years) of the loan, or at least the length over which the loan is amortized.

The following assumes a typical conventional loan where the interest is compounded monthly. First I will define two more variables to make the calculations easier:

• J = monthly interest in decimal form = I / (12 x 100)

• N = number of months over which loan is amortized = L x 12

Okay now for the big monthly payment (M) formula, it is:

```                              J
M  =  P  x ------------------------
1  - ( 1 + J ) ^ -N

where 1 is the number one (it does not appear too clearly on some browsers)
```

So to calculate it, you would first calculate 1 + J then take that to the -N (minus N) power, subtract that from the number 1. Now take the inverse of that (if you have a 1/X button on your calculator push that). Then multiply the result times J and then times P. Sorry, for the long way of explaining it, but I just wanted to be clear for everybody.

The one-liner for a program would be (adjust for your favorite language):

```         M = P * ( J / (1 - (1 + J) ** -N))
```

So now you should be able to calculate the monthly payment, M. To calculate the amortization table you need to do some iteration (i.e. a simple loop). I will tell you the simple steps :

Step 1: Calculate H = P x J, this is your current monthly interest
Step 2: Calculate C = M - H, this is your monthly payment minus your monthly interest, so it is the amount of principal you pay for that month
Step 3: Calculate Q = P - C, this is the new balance of your principal of your loan.
Step 4: Set P equal to Q and go back to Step 1: You thusly loop around until the value Q (and hence P) goes to zero.

```          Monthly Pmt = (P*(((1+i/200)^(1/6)-1))/(1-(((1+i/200)^(1/6)))^-(n*12)))
Where:
P = principal outstanding
i = annual interest rate percentage
n = number of years
```

Here is a easier to read representation:

```                           i    1/6
( 1 +  --- )       -   1
200
Pmt = Principal x  ------------------------
i   1/6    -12 x n
1 -  [ (1 + --- )     ]
200

Or to convert Canadian interest rates to US interest rates:

Can. Rate  1/6
US Rate =  1200 x [ ( 1 +  --------- )     - 1 ]
200

or as a formula, US Rate = 1200 * ((1 + Can.Rate/200)^(1/6) - 1)
```