## 13 Jun 2017

### Useful Shortcuts for Simple Interest & Compound Interest - IBPS Exams 2017

Useful Shortcuts for Simple Interest & Compound Interest - IBPS Exams 2017:
Dear Readers, Here we have given the Useful Shortcuts for Simple Interest & Compound Interest Problems for IBPS Exams 2017, candidates those who are preparing for the upcoming IBPS Exams 2017 can make use of it.

Simple Interest
Formula:
1) SI = P x R x T/100
2) Principal = Simple Interest ×100/ R × T
3) Rate of Interest = Simple Interest ×100 / P × T
4) Time = Simple Interest ×100 / P × R
5) If 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 years
R=Rate of interest (per year) in percentage

Type 1:
A sum of money is divided into n parts in such a way that the interest on the first part at r1% for t1 years, on second part at r2% for t2 years, on third part at r3% for t3 years and so on, are equal. Then the ratio in which the sum is divided in n part is:
1/r1 ×t1: 1/r2 ×t2: 1/r3 ×t3
Example:
A sum of Rs 7700 is lent out in two parts in such a way that the interest on one part at 20% for 5 yr is equal to that on another part at 9% for 6 yr. Find the two sums.
Solution:
Here, R1 = 20% R2 = 9%
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

Type 2:
Amount = Principal + S.I = p + [(p x r x t)/100]
Example:
What Principal will amount to Rs. 16000 in 6 years at 10% simple interest?
Solution:
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.
Principal should be Rs. 10000
Compound Interest
The difference between the amount and the money borrowed is called the compound interest for given period of time
1) Let principal =P; time =n years; and rate = r% per annum and let A be the total amount at the end of n years, then
A = P*[1+ (r/100)]n;
CI = {P*[1+ (r/100)]n -1}
2) When compound interest reckoned half yearly, then r% become r/2% and time n become 2n;
A= P*[1+ (r/2*100)]2n
3) For quarterly
A= P*[1+ (r/4*100)]4n
4) The difference between compound interest and simple interest over two years is given by
Pr2/1002 or P(r/100)2
5) The difference between compound interest and simple interest over three years is given by
P(r/100)2*{(r/100)+3}
6) When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively, Then total amount is given by
P ((1 + R1)/100) ((1 + R2)/100) ((1 + R2)/100)
7) Present worth of Rs. x due n years hence is given by
x/(1+R/100)

Type 1:
Interest is compounded half-yearly, therefore,
Example:
Find the compound interest on Rs. 20,000 in 2 years at 4 % per annum, the interest being compounded half-yearly.
Solution:
Principal = Rs. 20000, Rate = 2 % per half-year, Time = 2 years = 4 half- years
Amount=Rs.21648.64

Compound Interest = Total amount – Principal
= 21648.64 – 20000
= Rs. 1648.64

Type 2:
If interest is compounded annually,
Example:
Find compound interest on Rs. 8500 at 4 % per annum for 2 years, compounded annually.
Solution:
We are given:
Principal = Rs. 8500, Rate = 4 % per annum, Time = 2 years
= Rs. 9193.6
Compound Interest = Total amount – Principal
= 9193.6 – 8500
= 693.6
Compound Interest = Rs. 693.6

Type 3:
When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively. Then, Amount (= Principal + Compound interest) = P(1 + R1/100)(1 + R2/100)(1 + R3/100).
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 = 304
Hence the required compound interest is Rs.304.

Type 4:
When compound interest is reckoned half-yearly.
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.
Form the above we get
Example:
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
Amount = Rs
= Rs.16537.50

Difference between the compound interest and the simple interest
Example:
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?
Solution:
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