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Useful Shortcuts and Tricks for Simple Interest & Compound Interest
Simple Interest:
Formula:
1) SI = P x R x T/100Â
5) If the rate of Simple interest differs from year to year, then
Simple Interest = Principal × (R1+R2+ R3…..)/100
The four variables in the above formula are: SI=Simple Interest P=Principal Amount (This the amount invested)T=Number of yearsR=Rate of interest (per year) in percentage
T1 = 5 yr T2 = 6 yr
By using formula, ratio of two sums = 1/100 : 1/54 = 27 : 50
Therefore, first part = [27/(27+50)]*7700 = Rs 2700
Second part = [50/(27+50)]*7700 = Rs 5000
Let the principal be Rs. p, given rate of interest is 10% and time = 6 years.
Amount received at the end of 6 years = 16000 Rs.
=> 16000 = p + (p x 10 x 6)/100 = p + 6p/10 = 16p/10 => P = 16000 x (10/16) = 1000 x 10 = 10000 Rs.The principal should be Rs. 10000
3). If sum becomes n times in T yr at simple interest, then the formula for calculating the rate of interest
R =100(n-1) /T %
4). A sum of money becomes 4 times in 20 yr at SI. Find the rate of interest?
R =100(4-1)/20
=100*3 / 20 =5*3 =15
5). If A sum becomes n times in a certain rate of interest .then the time taken in which the same amount will be n times at the same rate of interest:
= (n-1)/2 × T (n = number of times)
6). If A sum becomes 3 times in a certain rate of interest in 5years .find the time taken in  the same amount will be 8 times at the same rate of interest:
=(8-1)/2*5
= 7/2 * 5
=17.5years
Useful Shortcuts and Tricks for Simple Interest & Compound Interest
Compound Interest
A = P*[1+ (r/100)]n;
A= P*[1+ (r/2*100)]2n
A= P*[1+ (r/4*100)]4n
Pr2/1002or P(r/100)2
P(r/100)2*{(r/100)+3}
P ((1 + R1)/100) ((1 + R2)/100) ((1 + R2)/100)
x/(1+R/100)
Useful Shortcuts and Tricks for Simple Interest & Compound Interest
Example Problems
Example:
Find the compound interest on Rs. 20,000 in 2 years at 4 % per annum, the interest is compounded half-yearly.Â
Solution:
Amount=Rs.21648.64
Compound Interest = Total amount – Principal
= 21648.64 – 20000
= Rs. 1648.64
Example:
Find the compound interest on Rs. 8500 at 4 % per annum for 2 years, compounded annually.Â
Solution:
We are given:
Principal = Rs. 8500, Rate = 4 % per annum, Time = 2 years
= Rs. 9193.6Compound Interest = Total amount – Principal= 9193.6 – 8500
= 693.6Compound Interest = Rs. 693.6
Example:
Find the compound interest on a principal amount of Rs.5000 after 2 years, if the rate of interest for the 1st year is 2% and for the 2nd year is 4%.
Solution:
Here R1 = 2% R2 = 4% and p = Rs.5000, we have to find CI (compound interest).
CI = 5000(1 + 2/100)(1 + 4/100) – 5000
= 5000 x (102/100)(104/100) – 5000
= 5000 x (51/50) x (52/50) – 5000
= 5000 x (51 x 52/2500) – 5000
= 5000 x (2652 / 2500) – 5000
= 5304 – 5000 = 304Hence the required compound interest is Rs.304.
If the annual rate is r% per annum and is to be calculated for n years, then, in this case, rate = (n/2%) half-yearly and time = (2n) half-yearly.
Sam investment Rs.15,000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be.
Solution:
P = Rs. 15000; R = 10% p.a = 5% half-year, T = 1 year = 2 half year
If the simple interest for a certain sum for 2yrs at the annual rate of interest R% is SI. Then,
Compound interest (CI) = SI (1+r/200)Â Â (no. of years =2)
5). If the simple interest for a certain sum for 2 yr at 5%pa is 200, then what will be the compound interest for the same sum for the same period and the same rate of interest?
Solution:
SI =200 r=5%
CI =200(1+5/200) =200*(205/200) =205
If a certain sum at compound interest becomes x times n1^yr and y times n2^yr then,
X1/N1 = Y1/N2
Useful Shortcuts and Tricks for Simple Interest & Compound Interest
6). If an amount at compound interest becomes twice in 5yr, then in how many years, it will be 16 times at the same rate of interest?
21/5Â = 16 1/x2
=24*1/x2
1/5 = 4/x2
X2 = 5*4 =20yrs
If a certain sum at compound interest amounts to A1 in  n yrs and A2 in (n+1) yrs,
then
Rate of compound interest =(A2 – A1)/A1 *100%
Sum = A1 (A1 /A2)n
7). Â A sum of money invested at compound interest amounts to 800 in 2yr and 840 in 3yrs. Find the rate of interest and the sum.
A1 =800 ; A2 =840,
Rate of interest = (840-800)/800 *100% =40/8 =5%
Sum = 800 *(800/840)2 =320000/441 = Rs.725.62
If the populations of a city P and increases with the rate of R% per annum, then
- Populations after n yr = p(1+R/100)n
- Populations n yr ago = p / (1+R/100)n
8). The population of city A is 5000. It increases by 10% in 1st year. It decreases by 20% in the 2nd yr because of some reason. In the 3rd yr, the population increases by 30%. What will be the [population of area A at the end of 3yrs?
=5000(1+10/100)(1-20/100)(1+30/100)
= 500*(11/10)*(4/5)*(13/10) = 5720
Difference between ci and si 2yr =pr2 /1002Â Â Â
9). The difference between c.i and s.i for 2yr at the rate of 5% per annum is 5 .then the sum
5 = p (5/100)2 = Rs.2000
Rate of interest (no .of years =2)
(for only ci)
2% = 4.04%
3% = 6.09%
4% = 8. 16%
5% = 10.25%
6% = 12.36%
7%Â Â = 14.49%
8% = 16.64%
9% = 18.81%
10%= 20.00
+ 1.00 =21%
10). What is the Compound interest for Rs. 1500 at 5% rate of interest for 2 years?
1500*(10.25/100) =153.75
Difference between the compound interest and the simple interestÂ
If the difference between the compound interest and the simple interest on a certain sum of money at 5% per annum for 3 years is Rs. 1220. What is the sum?