How To intuit Loan Payments and Amortization on the Back of an Envelope With a Cheap Calculator

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In a previous article we presented a uncomplicated formula to suspect the estimate of a monthly home mortgage loan payment. The formula applies to any mixture interest loan. The only extra tool you need is a calculator with a power function key. That's the key with the y superscript x (y ^ x). If you have kids in school you probably already have one.

Here is a communicate of monthly cost formula.

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The variables are:

N = loan period in months. I.e. 20 years = 240 months.

R = interest rate in whole numbers. I.e. 8% written as 8.

P = requisite estimate of the loan. The estimate borrowed.

Q = the Q factor. An intermediate calculation.

M = monthly cost amount

Here's the entire formula for the monthly cost estimate of a mixture interest loan:

M = (P * R * Q) / (1200 * (Q -1))

Easy enough, but first you have to suspect the value of Q. Here is the formula:

Q = (1 + R/1200) ^N. Pretty simple, but you do need the power function key. N can get large.

In our earlier example we calculated a monthly cost of 8.22 on a ,000 second mortgage at 8% for 20 years. You have paid the 2nd mortgage loan for 5 years (60 months). The pay off estimate is ,763 (rounded). This is how to suspect the pay off estimate on any mixture interest loan after N estimate of payments.

This is an easy three step process with a subtraction at the end. First suspect the increase value of the loan estimate (P). P increases by a factor of (1 + R/1200) per month, so after N months the value of the requisite estimate of the loan would have inflated to P * (1 + R/1200) ^ N. For the current ,000 second mortgage the calculation looks like this:

50000 * (1 +8/1200) ^60 = 74492.28 (step one)

The monthly payments have also inflated by a factor of (1 + R/1200) per month so in math talk we have a geometric series with n terms. The monthly cost part is a miniature more involved and the formula looks like this:

1200 * M * ((1 + R/1200) ^N -1) / R

Plug in the actual values and it looks like this:

1200 * 418.22 * (1 + 8/1200) ^60 / 8 = 30729.49 (step two)

Now desist up by subtracting the inflated repayment value from the inflated loan estimate value to get the pay off amount:

74492.28 - 30729.49 = 43762.79 (pay-off)

Once you know how to suspect the monthly cost and pay-off estimate for any mixture interest loan on the back of an envelope, you can noodle mortgage and car loan what-ifs from anywhere.

How To intuit Loan Payments and Amortization on the Back of an Envelope With a Cheap Calculator