In a previous report we presented a easy recipe to calculate the estimate of a monthly home mortgage loan payment. The recipe applies to any compound interest loan. The only special 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 retell of monthly payment formula.
Calculate Mortgage Interest
The variables are:
N = loan duration in months. I.e. 20 years = 240 months.
R = interest rate in whole numbers. I.e. 8% written as 8.
P = critical estimate of the loan. The estimate borrowed.
Q = the Q factor. An intermediate calculation.
M = monthly payment amount
Here's the whole recipe for the monthly payment estimate of a compound interest loan:
M = (P * R * Q) / (1200 * (Q -1))
Easy enough, but first you have to calculate 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 payment 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 calculate the pay off estimate on any compound interest loan after N estimate of payments.
This is an easy three step process with a subtraction at the end. First calculate 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 critical 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 payment part is a little more complex and the recipe 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 halt up by subtracting the inflated reimbursement 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 calculate the monthly payment and pay-off estimate for any compound interest loan on the back of an envelope, you can noodle mortgage and car loan what-ifs from anywhere.
How To speculate Loan Payments and Amortization on the Back of an Envelope With a Cheap Calculator Calculate Mortgage Interest
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