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Quantitative Aptitude > Simple and Compound InterestAdd Comment Bookmark share + Refresher MaterialInterest is earned when money is given to someone else to use, for example if it is deposited with a bank
Simple Interest
Simple Interest is interest earned on the principal only. In other words, interest income will be distributed A = P + (P x r x t) Bozo put As. 1,000 in the bank for 6 months at a 10% interest rate. Find how much money will he have in
Compound Interest
In simple interest, you earn interest payments from the principal only. In Compound Interest, you reinvest Let us say you are investing Rs. 1,000 at 10% compound interest. After a specified period of time, called The period of compounding is important because as the period of compounding becomes lesser, the interest amount joining the capital becomes higher.
The equation for finding compound interest is: A = P (1 + r/k) ^{kxn} Simple Interest:
Compound Interest: A = ( 1 + r/k ) ^{kxn} A = ( 1 + 0.1/2 ) ^{2*5} A = 1,000 (1 + 0.05) ^{10} A = 1,000 x 1.62889
THE RULE OF 72
The rule of 72 is a quick way to show how long it will take to double your money under
Here are more examples: At 6%, it will take 12 years ( 72/6 = 12 ) At 12%, it will take 6 years ( 72/12 = 6 ) The rule of 72 is a short cut to estimate the magic of compound interest that makes your money grow.
For a principal amount P, we have:
Net Present Value
This is an important concept used in financial analysis. The basic principle underlying this concept is that The money received or paid today can be invested by the receiver to earn interest. Suppose Ram had to pay Re1 to Shyam after an year, he could also pay Re 0.91 to Shyam now if 10% If a company is expected to earn Rs A1 in year 1, Rs A2 in year 2, Rs A3 in year 3…. and Rs An in year
If the earnings are same every year (A1 = A2 = …………..An = A) This is used to calculate monthly instalments in instalment schemes offered by dealers. Then V = (EMI) [(1+r) ^{n}1] / [r] [1+r] ^{n} So EMI = Vr(1+ r) ^{n}/ (1+ r) ^{n}1 Interest Rate On Instalment
POPULATION FORMULA If population is P and annual increase is r%, then population at the end of t years is P (1 + r/100) ^{t}
SOLVED EXAMPLES QUESTION
Find the simple interest on Rs 400 for 5 years at 6 per cent
SOLUTION
SI = 400 x 5 x 6/100 = Rs 120
QUESTION
The simple interest on a sum of money is 1/9 of the principal, and the number of year is equal to the rate per cent per annum. Find the rate per cent.
SOLUTION
Let Principal = P, time = t years, rate = t So t ^{2 } = 100/9 So t = 10/3 = 3 1/3%
QUESTION
A sum of money doubles itself in 10 years at simple interest. What is the rate of interest?
SOLUTION
Let the sum be Rs 100. Then rate = (100 x 100) / (100 x 10) = 10%
QUESTION
A sum of money doubles itself in 7 yrs. In how many years will it become fourfold?
SOLUTION
Rate = (100 * 100 ) / Pt = 100 / 7 So Time = 100 ( 41 ) / 100 / 7 = 21 years
QUESTION
A lent Rs 600 to B for 2 years, and Rs 150 to C for 4 years and received altogether from both Rs 90 as interest. Find the rate of interest, simple interest being calculated.
SOLUTION
Rs 600 for 2 years = Rs 1200 for one year. So Rate = (90 * 100) / (1800 * 1) = 5%
QUESTION
The rate of interest for the first 2 yrs is 3% per annum, for the next 3 years is 8% per annum and for the period beyond 5 years 10% per annum. If a man gets Rs. 1520 as a simple interest for 6 years, how much money did he deposit?
SOLUTION
Let his deposit = Rs 100
QUESTION
A sum of money triples itself in 20 yrs at SI. Find the rate of interest.
SOLUTION
Rate = 100 (3 –1)/20 =10%
QUESTION
In what time does a sum of money become four times at the simple interest rate of 5% per annum?
SOLUTION
Using the formula,
QUESTION
A certain sum of money amounts to Rs 756 in 2 yrs and to Rs 873 in 3.5 yrs. Find the sum and the rateof interest.
SOLUTION
P + SI for 3.5 yrs = Rs 873
QUESTION
A sum was put at SI at a certain rate for 2 yrs. Had it been put at 3% higher rate, it would have fetched Rs 300 more. Find the sum.
SOLUTION
Let the sum be Rs x and the original rate be y% per annum. Then, new rate = (y + 3)% per annum.
QUESTION
At a certain rate of simple interest Rs 800 amounted to Rs 920 in 3 years. If the rate of interest be increased by 3%, what will be the amount after 3 years?
SOLUTION
First rate of interest = (120 x 100) / ( 800x3 ) = 5%
QUESTION
Rs 4000 is divided into two parts such that if one part be invested at 3% and the other at 5%, the annual interest from both the investments is Rs 144. Find each part.
SOLUTION
Let the amount lent at 3% rate be Rs x, then
QUESTION
A sum of Rs 2600 is lent out in two parts in such a way that the interest on one part at 10% for 5 years is equal to that on another part at 9% for 6 years. Find the two sums.
SOLUTION
Each Interest = (1st Part) x (5) x (10/100) = (2nd Part) x (6) x (9/100)
QUESTION
A certain sum of money amounts to Rs 2613 in 6 yrs at 5% per annum. In how many years will it amount to Rs 3015 at the same rate?
SOLUTION
Use the formula:
2010 = (100 x 3015) / (100 + 5t )
QUESTION
A person lent a certain sum of money at 4% simple interest; and in 8 years the interest amounted to Rs 340 less than the sum lent. Find the sum lent.
SOLUTION
Let the sum be Rs. x.
QUESTION
The difference between the interest received from two different banks on Rs 500 for 2 yrs is Rs 2.5. Find the difference between their rates.
SOLUTION
I _{1} = (500) x (2) x (r _{1}/100) = 10 r _{1}
QUESTION
The simple interest on a certain sum of money at 4% per annum for 4 yrs is Rs 80 more than the interest on the same sum for 3 yrs at 5% pr annum. Find the sum.
SOLUTION
Let the sum be Rs X , then at 4% rate for 4 yrs the simple interest = (x) x (4) x (4) / 100 = Rs 4x / 25 At 5% rate for 3 yrs the simple interest =
QUESTION
Ramesh borrows Rs 7000 from a banks at SI. After 3 yrs he paid Rs 3000 to the bank and at the end of 5 yrs from the date of borrowing he paid Rs 5450 to the bank to settle the account. Find the rate of interest.
SOLUTION
Any sum that is paid back to the bank before the last instalment is deducted from the principal and not from the interest. Thus, Total interest = (Interest on Rs 7000 for 3 yrs) + Interest on (Rs 7000 – Rs 3000 =) Rs 4000 for 2 yrs.
QUESTION
At what rate per cent compounded yearly will Rs 80,000 amount to Rs 88,200 in 2 yrs?
SOLUTION
We have 80,000 ( 1 + r/100 ) ^{2} = 88,200 Or, ( 1+ r/100 ) ^{2} = 88200 / 80000 = 441 / 400 = ( 21 / 20 ) ^{2} Or, (1 + r/100) = 21/20 So r = 5%
QUESTION
A sum of money placed at compound interest doubles itself in 4 yrs. In how many years will it amount to eight times itself?
SOLUTION
We have P (1 + r/100) ^{4} = 2P So (1 + r/100) ^{4} = 2
QUESTION
A sum of money at compound interest amounts to thrice itself in three years. In how many years will it be 9 times itself?
SOLUTION
Detail Method: (3) ^{2} = {( 1 + r/100 ) ^{3}} ^{2} or 9 = ( 1 + r/100 ) ^{6} So the sum x will be 9 times in 6 years.
QUESTION
At what rate per cent compound interest does a sum of money become ninefold in 2 years?
SOLUTION
Detail method: let the sum be Rs x and the rate of compound interest be r% per annum; then
QUESTION
In what time will Rs 390625 amount to Rs 456976 at 4% compound interest?
SOLUTION
QUESTION
Find the least number of complete years in which a sum of money at 20% CI will be more than doubled
SOLUTION
QUESTION
The CI on a certain sum is Rs 104 for 2 yrs and SI is Rs 100. What is the rate per cent ?
SOLUTION
Difference in CI and SI = 104 – 100 = Rs 4.
QUESTION
An amount of money grows upto Rs 4840 in 2 yrs and upto Rs 5324 in 3 yrs on compound interest. Find the rate per cent.
SOLUTION
We have, P + CI of 3 yrs = Rs 5324———(1)
QUESTION
A certain amount of money at compound interest grows upto Rs 51168 in 15 yrs and upto Rs 51701 in 16 yrs. Find the rate per cent per annum.
SOLUTION
Rate = (51701  51168) x 100 / 51168 = (533 x 100) / 51168 = 100 / 96 = 25 / 24 = 1 1/24 %
QUESTION
Find the compound interest on Rs 18,750 in 2 yrs, the rate of interest being 4% for the first year and 8% for the second year.
SOLUTION
After first year the amount = 18750 {(1 + 4) / 100} = 18750 (104/100) After 2nd year the amount = 18750 (104/100) (108/100)
QUESTION
Rs 4800 becomes Rs 6000 in 4 years at a certain rate of compound interest. What will be the sum after 12 years?
SOLUTION
The above equation shows that Rs 4800 becomes Rs 9375 after 12 years.
QUESTION
A man borrows Rs 3000 at 10% compound rate of interest. At the end of each year he pays back Rs 1000. How much amount should he pay at the end of the third year to clear all his dues?
SOLUTION
The general formula for the above question may be written as: If a man borrows Rs P at r% compound interest and pays back Rs A at the end of ach year, then at the end of the nth year he should pay Rs In the above case:
QUESTION
A sum of money is lent out at compound interest rate of 20% per annum for 2 years. It would fetch Rs 482 more if interest is compounded halfyearly. Find the sum.
SOLUTION
Suppose the sum is Rs P.
QUESTION
The simple interest on a sum at 4% per annum for 2 yrs is Rs 80. Find the compound interest on the same sum for the same period.
SOLUTION
Rate = (2 xDiff inCI& SI) / (SI) x 100
QUESTION
The compound interest on a certain sum of money for 2 years at 10% per annum is Rs 420. Find the simple interest at the same rate and for the same time.
SOLUTION
QUESTION
The compound interest on a certain sum for 2 yrs is Rs 40.80 and simple interest is Rs 40.00. Find the rate of interest per annum and the sum.
SOLUTION
A little reflection will show that the difference between the simple and compound interests for 2 yrs is the interest on the first year’s interest.
QUESTION
If the CI on a certain sum for 2 yrs at 3% be Rs 101.50, what would be the SI?
SOLUTION
CI on 1 rupee = ( 1+ 3/100 ) ^{2}  1 = (103/100) ^{2} – 1 = Re 609/10000 SI on 1 rupee = Rs (2) x (3 /100) = Re 6/100
QUESTION
If the simple interest on a certain sum of money for 3 yrs at 5% is Rs 150, find the corresponding CI.
SOLUTION
Whenever the relationship between CI and SI is asked for 3 yrs of time, we us the formula:
QUESTION
The difference between the compound interest and the simple interest on a certain sum of money at 5% per annum for 2 years is Rs 1.50. Find the sum.
SOLUTION
Sum = 1.5 (100 / 5) ^{2} = 1.5 x 400 = Rs 600
QUESTION
Divide Rs 3903 between A and B, so that A’s share at the end of 7 yrs may equal B’s share at the end of 9 yrs, compound interest being at 4%.
SOLUTION
We have, (A’s share at present) (1 + 4 /100) ^{7}
QUESTION
The difference between the simple and the compound interests on a certain sum of money for 2yrs at 4% per annum is Re 1. Find the sum.
SOLUTION
Sum = Difference (100/r) ^{2} = 1(100/4) ^{2} = Rs 625
QUESTION
If the difference between CI and SI on a certain sum of money for 3yrs at 5% p.a. is Rs 122, find the sum
SOLUTION
Sum = [(122) x (100) x (100)x (100) / {5 ^{2} (300 + 5)}] = Rs 16,000
QUESTION
Find the difference between CI and SI on Rs 8000 for 3 yrs at 2.5% p.a
SOLUTION
Difference = (Sum) x (r ^{2}) (300 + r) / (100) ^{3} = 8000 x 2.5 x 2.5 (300 + 2.5) / 100 x 100 x 100
QUESTION
Find the compound interest on Rs 10000 for 3 years if the rate of interest is 4% for the first year, 5% for the second year and 6% for the third year.
SOLUTION
The Compound Interest on Rs x in ‘t’ years if the rate of interest is r1% for first year, r2% for the second year …. .and rt% for the tth year is given by
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