A worked exmaple of - A persian folk method of figuring interest

Created: by Pradeep Gowda Updated: Nov 10, 2020 Tagged: mathematics

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) is:

C = r * (1 + r )^N * P / ((1 + r )^N - 1)

where,

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.