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# Compound Interest Shortcuts and Tricks

### CI Formulae:

1. Amount = P[1+(r/100)]
1. Compound Interest (CI) = P [ (1+r/100)t -1 ].
1. Simple Interest (SI) = (CI * rt) / 100 [(1+r/100)t -1].
1. When the difference between SI and CI on the certain sum for 2 years at r% is d Rs.  Sum = (d/r2 )*1002.

When the difference between SI and CI on a certain sum for 3 years at r% is d Rs.

Sum = [d(100)3 / r2(300+r)].

1. If a sum A becomes B in t1 years at CI. Then After t2 years,

Sum = (B)t2 / t1 /(A)(t2 / t1)-1.

1. The rate of Interest = [ (Difference of amount after n years and (n+1) years )/ Amount after n years ]*100.

## Shortcut Tricks to Solve Compound Interest Problems

### Solving CI Problems using smart tricks:

Problem 1: What will be the compound interest on 5000 Rs. For 2 years at the rate of 12% p.a.?

Sol: From percentage formula Net percentage = (a+b+ab/100)%
= [12+12+(12*12)/100]%.
= [24 +1.44]%
= 25.44%.
We know, 100%(means principle) à 5000.
25.44% à ?
è(25.44 *5000)/100 = 1272.

Problem 2: A sum of money invested at compound interest amounts to 800Rs. in 3 years and Rs. 882 in 5 years. What is the rate of interest?
Sol:  [  In the case of Simple interest
[Am –An] years. ]
But Here,   In the case of Compound Interest[ Am / An ] years = Am-n years.

• P(1+R/100)5 / P(1+R/100)3 = 882/800.
• (1+R/100)2 years =441/400.
• 1+R/100 =21/20.
• 100+ R= (21/20)*100
• R=5%.

Problem 3: On a particular amount the CI at the end of the year is 40Rs/- and in the 2nd year is 42 Rs/-.How much money was deposited?
Sol: Rate of interest  = [(Final- Initial)/Initial] *100.
= [(42 40)/40] *100 =(2/40)*100 = 5%.
We know, 5% à 40,
100% à?
P = (100 *40)/5 = 800.

Problem 4: When time period T is given infraction at CI  i.e. T= 3 ¾ years.
Amount = P[(1+R/100)3 (1+(3/4 R)/100 )].

Problem 5: On What is the difference between CI and SI for the sum of 20000 over 2 years period. If compound interest is calculated at 20% p. a. and SI at 23% p.a.
Sol:  RSI  = 23% , Net % for 2 years = 23+23 =46%.
RCI = 20% , Net % for 2 years  = 20+20+(20*20)/100 = 44%
Difference of SI –CI = 46-44 = 2%.
If 100% à 20000 ( principle amount is always taken as 100%)
Then  2% à ?
i.e. (2 * 20000)/100 = 400.

Problem 6: A bank offers 5% CI on half year basis customer deposit 1600 Rs each on 1st July of a year at the end of the year What is the interest?
Sol: CI = [ [2.5 + 2.5 +(2.5* 2.5)/100]+[2.5] ]*1600