I found the paper “A persian folk method of figuring interest” via Dr Peyman Milanfar on twitter, where he described this method as the one deployed by his father to quickly calculate the monthly payments on a home loan.
I thought it is a good idea to do a workout of the formula myself so that I can remember it:
For this demonstration, let’s consider a loan amount (Principal) of $10,000 for a period of 4 years(48 months) at an interest rate of 7% pa.
Step 1: calculate the interest amount over the loan period
Interest = 0.5 * Principal * Number of years * Annual Interest Rate Interest = 0.5 * 10000 * 4 * 0.07 Interest = 1400.0
Step 2: calculate the Monthly Payment
Monthly Payment = (Principal + Interest) / (Number of Months) Monthly Payment = (10000 + 1400.0) / 48 Monthly Payment = 237.5
Applying the actual mortagage formula for Monthly Payment (
C = r * (1 + r )^N * P / ((1 + r )^N - 1)
r = monthly interest rate => 0.07 / 12 N = total number of months => 48 P = principal => 10,000
therefore we have,
C = 239.46
The shortcut method is a very good approximation of the true calculation, and it is made of simple arithmetic operations available on any handheld calculator / phone.
This is surprisingly handy when you are at a negotiating table (eg: Car purchase). This is the kind of mentral tricks that are really useful in the “real world”. Try it out.
Update: The original paper is a page long, so I put the image here:
Credit: Dr Peyman Milanfar.