How To Calculate Loan Payments And Amortization On The Back Of An Envelope With A Cheap Calculator

In a previous article, we presented a simple formula for calculating the monthly payment amount for a home mortgage loan. The formula applies to any compound interest loan. The only special equipment you need is a calculator with a power function key. That’s the key with the superscript yx (y ^ x). If you have kids in school, you probably already have one.

Here is a review of the monthly payment formula.

The variables are:

N = loan period in months. that is, 20 years = 240 months.

R = interest rate in whole numbers. that is, 8% written as 8.

P = principal amount of the loan. The amount borrowed.

Q = the Q factor An intermediate calculation.

M = monthly payment amount

Here is the complete formula for the monthly payment amount for a compound interest loan:

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

It’s pretty easy, but first you have to calculate the value of Q. Here’s the formula:

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

In our example above, we calculated a monthly payment of $ 418.22 on a $ 50,000 8% second mortgage over 20 years. You have paid the 2nd mortgage loan for 5 years (60 months). The amount to be paid is $ 43,763 (rounded). This is how the payoff amount for any compound interest loan is calculated after N number of payments.

This is a simple three-step process with a subtraction at the end. First calculate the growth value of the loan amount (P). P increases by a factor of (1 + R / 1200) per month, so after N months, the value of the principal amount of the loan would have inflated to P * (1 + R / 1200) ^ N. For the $ 50,000 current second mortgage the calculation looks like this:

50,000 * (1 +8/1200) ^ 60 = 74492.28 (step one)

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

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

Plug in the actual values ​​and it will look like this:

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

Now finish by subtracting the inflated repayment value from the inflated loan amount value to get the payment amount:

74492.28 – 30729.49 = 43762.79 (payment)

Once you know how to calculate the monthly payment and payoff amount for any compound interest loan on the back of an envelope, you can mortgage noodles and auto loans from anywhere.