# Vedic method to calculate Compound Interest using back of the envelope

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

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 = **I¹**

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 1**0*** *= 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**