Vedic method to calculate Compound Interest using back of the envelope

Rohit Talukdar
3 min readJan 1, 2024

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Today I learned(TIL) a quickly way to calculate Compound interest. Initially using just a paper and pen and eventually (hopefully) in my head.

Conventional method for calculating Compound Interest

The traditional method to calculate compound interest follows the formula

A = P x (1+R)^n where
A is the final amount after interest for n years
P is the Principal or initial amount
R is the rate of interest and
n is the number of years
but it needs a calculator to

Example
Lets calculate Compound Interest for 3 years at 7% for Rs 6000.
The traditional method involves
A = Rs 6000 x (1 + 7/100)³ = 6000 x (107/100)³= 6000 x 1.07³ = 6000 x 1.225043 = Rs 7350.258
The interest then is CI = A-P = Rs 7350.258–7000 = Rs 1350.258

Contrast it to the Vedic method for calculating Compound Interest

Interest for 1st year = a x 7%(P) = Lets call 7%(P) as I¹
Interest for the 2nd year = b x 7%(I¹) = lets call this I²
Interest for the 3rd year = c x 7%(I²) = lets call this I³

Total Interest = I¹ + I² + I³
How to get the values for a, b and c ? Use the pattern table below

Pattern For Compound Interest : src youtube video

In the table above, n=3 yrs, so we choose the 3rd row where the values are {1,3,3,1}. Ignoring the first column(which is all 1's) in each row and lets only consider the the remaining columns {3,3,1}.
So a,b,c are a=3, b=3 and c=1

Translating the formula into values, for 3 years

Interest for 1st year = a x 7%(P) = 3 x 7%(6000) = 3 x 420 = 1260 =
Interest for the 2nd year = b x 7%(I¹) = 3 x 7%(420) = 3 x 29.4 = 88.2 = I²
Interest for the 3rd year = c x 7%(I²) = 1 x 7%(29.4) = 1x 2.058 = 2.058 = I³

So total interest = I¹ + I² + I³ = 1260 + 88.2 + 2.058 = 1350.258

Let’s take a 2nd example

If a bank lends 100 at 10% interest for 10 years what would be the amount after 10 years ?

From MathIsFun, 100 compounding at 10% for 5 yrs = 161.05
Now lets try the same using vedic maths
First lets get coefficient values for a,b,c,d,e, which from the pattern table is {5,10,10,5,1}

Interest for 1st year = a x 5%(P) = 5 x 10%(100) = 5 x 10 = 50 = I¹
Interest for the 2nd year = b x 10%(I¹) = 10 x 10%(10) = 10 x 1 = 10 = I²
Interest for the 3rd year = c x 10%(I²) = 10 x 10%(1) = 10 x 0.1 = 1 = I³
Interest for the 3rd year = d x 5%(I³) = 5 x 10%(0.1) = 5 x 0.01 = 0.05 = I⁴
Interest for the 3rd year = e x 10%(I⁴) = 1 x 10%(0.1) = 0.01 = I⁵

So Total Interest CI = I¹ + I² +I³ + I⁴ + I⁵ = 50 + 10 + 1 + 0.05 + 0.01 = 61.06
So A = Principal(P) + Compound Interest (CI) = 100 + 61.06 = 161.06

Summary
As long as we remember the Compund Table pattern table or the powers of 11, we can use this method to get CI on the back of an envelope.

References

  1. Youtube: Compound Interest Mentally by Kuldeep Singh
  2. Vedic Maths Newsletter on vedicmaths.org

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