Quicker Maths

## Rule of 72 – Estimation of Compound Interest and Time

Posted on November 20, 2011

Effect of Compounding

The Rule of 72 is a good quick math shortcut to find out the following –

• Time required for an amount to double itself, at a given rate of interest
• Rate at which an amount should grow to double itself in given time

This formula can be applied for “Doubling Problems” related to money, population, etc. which grows at an annual compounded rate.

Formulae

1. To calculate the time; T = 72/R
2. To calculate the rate of interest; R= 72/T

T = Time required to double a sum of money at the rate of R% per annum.

R = Rate of interest at which a sum of money gets doubled in T years.

Explanation of the formula

To find out the number of years required to double an investment in a fixed deposit which gives you 9% rate of interest compounding annually, divide 72 by 9.

For example, if you invest Rs. 10000 with compounding interest at a rate of 9% per annum, the rule of 72 gives 72/9 = 8 years required for the investment to become Rs. 20000; an exact calculation gives 8.0432 years. So there is small margin of approximation.

The above formula is more accurate at lower interest rates (say up till 10%). The approximation error starts increasing after that.

In case of continuous compounding, 69 instead of 72, gives more accurate results. However, in our day to day life the concept of continuous compounding is rarely used.

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#### Posted by Vineet Patawari

1. how to learn log problems

2. ?? ??????? ??? ?? ???? ?? ??? ??? ?? ????? ???? ??? ?? ???? ?? ???? ??????? ??????? ?????? (??+1)^ ??? *??????? ?????? ???? ?? ” ????? ??? ?????” ?????? ?? ?? ????? ?? ??? ???

3. ???? ????? ???? ??? ???? ????? ????? ??? ?????? ????? ?? ?????? ??? ???? ???? ?????? 72 ?? ????? ?? ?? ?? ??? ???? ?? ??? ? ??????? ?????? ???? ?? ????? ??? ????? ?????? ?? ?? ????? ?? ??? ???

4. is there any shortcut to solve men and work problems

• Yes, there have about five short cut methods to solve questions of men and work. Please ask your doubt question. Kisku Sir, SURE SUCCESS, BHUBANESWAR, ODISHA.

• how can i contact kisku sir

• SIR PLEASE REFER A GOOD BOOK ON QUANTITATIVE APTITUDE

• i have a trick…..

5. Average Problem : A man bowling average is12.4 take wickets for 26 runs and thereby decreases his average by 0.4.The no of wickets taken by him before his last match was ?

• data insufficient .. i tried googling the question u gave ..
it shud hav been 26 runs for 5 wickets ..
then ans is 85 !

• yes sir it was 5 wickets I LATER SEE MY ASSIGNMENT .The answer is 85

• bowling avg=(total runs)/total wickets

let wickets before last match is x

(12.4*x + 26)/x+5=(12.4- 0.4)

(12.4*x + 26)/x+5=12

x=85

6. Please solve this Problem on Average : There was one Mess for 30 boarders in a certain hostel .on the no of boarders being increased bu10, the expenses of the mess were increased by Rs 40per month while the average expenditure diminished by 2.Find the orignal monthly Expenditure ?

• 30x + 40 = (30+10)*(x-2)
40x – 30x = 120
x = 12

original monthly expenditure = 30*12 = 360

7. is there any sort trick to count a sum of compound interest ??

i know this A=P(1+R/100)N/T

• We all know the traditional formula to compute compound interest.
CI = P*(1+R/100)^N – P

This calculation gets very tedious when N>2 (more than 2 years). The method suggested below is a very simple way to get CI/Amount after ‘N’ years.

You need to recall the old Pascal’s Triangle in following way:
Code:

Number of Years (N)
——————-
1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
. 1 …. …. … … 1

Example: P = 1000, R=10 %, and N=3 years. What is CI & Amount?

Step 1: 10% of 1000 = 100, Again 10% of 100 = 10 and 10% of 10 = 1
We did this three times becoz N=3.

Step 2:
Now Amount after 3 years = 1 * 1000 + 3 * 100 + 3 * 10 + 1 * 1 = Rs.1331/-
The co-efficients – 1,3,3,1 are lifted from the pascal’s triangle above.

Step 3:
CI after 3 years = 3*100 + 3*10 + 3*1 = Rs.331/- (leaving out first term in step 2)

If N =2, we would have had, Amt = 1 * 1000 + 2 * 100 + 1 * 10 = Rs. 1210/-
CI = 2 * 100 + 1* 10 = Rs. 210/-

This method is extendable for any ‘N’ and it avoids calculations involving higher powers on ‘N’ altogether!

A variant to this short cut can be applied to find depreciating value of some property. (Example, A property worth 100,000 depreciates by 10% every year, find its value after ‘N’ years).

N.B Prefer this method if N>=3. It will always work and it will save your time like anything.