Simple interest and compound interest problems are very important in all entrance exams. When a person or bank lends money to a borrower, the borrower usually has to pay an extra amount of money to the lender. This extra money is called interest. Simple interest is based on the principal amount of a loan or deposit, while compound interest is the interest that is added to the principal at the end of the each period to arrive at the new principal for the next period. Under compound interest, the amount at the end of the first year will become principal for the second year; the amount at the end of the second year becomes the principal for the third year and so on.

1. The simple Interest on a certain sum of money at the rate of 4% p.a. for 5 years is Rs. 1680. At what rate of interest the same amount of interest can be received on the same sum after 4 years ?

a) 5% b)6% c)7% d)8%

2. The interest on a certain deposit at 4.5% p.a. is Rs. 405 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a. ?

a)Rs.50 b) Rs. 45 c)Rs.40.5 d)Rs. 48.5

3. Mr.Govind invested an amount of Rs.13900 divided in two different schemes S1 and S2 at the simple interst rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in two years was Rs.3508, what was the amount invested in Scheme S2?

a) Rs.6400 b)Rs.6500 c) Rs.7200 d) Rs.7500

4. A sum of money was invested in a bank at 8% simple interest p.a. for 3 years. Instead had it been invested in mutual fund at 8.5% p.a. simple interest for 4 years, the earning would have been Rs.500 more. What is the sum invested?

a) Rs.4500 b) Rs.5000 c) Rs.3500 d) Rs. 5500

5. A person borrowed Rs.600 @ 3% per annum S.I and Rs.800 @ 4½ % per annum on the agreement that the whole sum will be returned only when the total interest becomes Rs.246. The number of years, after which the borrowed sum is to be returned, is

a) 2 years b) 3years c) 4 years d) 5 years

6. A sum of Rs.13000 is divided into three parts such that the simple interests accrued on them for two, three and four years respectively may be equal. Find the amount deposited for 4 years.

a)5000 b) 6000 c)4000 d)3000

7. A sum of Rs.100 is lent at simple interest of 3% p.a. for the first month, 9% p.a. for the second month, 27% p.a. for the third month and so on. What is the total amount of interest earned at the end of the year approximately

a) Rs.797160 b) Rs.791160 c)Rs.65930 d) Rs.66430

8. If the simple interest on a sum of money at twelve percent per annum for two years is Rs.3800, compound interest on the same sum for the same period at the same rate of interest is

a) Rs.4028 b)Rs.4100 c)Rs.4128 d) 4228

9. A sum of money is borrowed and paid back in two annual installments of Rs.882 each allowing 5% compound interest. The sum borrowed was :

a) Rs.1620 b) Rs. 1640 c)Rs.1680 d)Rs.1700

10. Rakesh invested an amount of Rs.12000 at the rate of 10% simple interest and another amount at the rate of 20% simple interest. The total interest earned at the end of one year on the amount invested became 14 p.c.p.a. Find the total amount invested .

a) Rs.20000 b)Rs.22000 c) Rs.24000 d) Rs.25000

11.The rate fo simple interest in two banks is in the ratio of 4 : 5 . Amith wants to deposit his total saving in these two banks in such a way that he should receive equal half yearly interest from both. He should deposits the saving in the banks in the ratio of:

a) 2 : 5 b)5 : 4 c) 5 : 3 d)4 : 5

12. A sum of money becomes triple itself in 16 years. In how many years will it become 5 times at the same rate?

a) 32 b) 15 c) 27 d) 30

13. The compound interest on Rs.30,000 at 7% per annum is Rs. 4347. The period (in years) is:

a) 2 b) 2 ½ c) 3 d) 4

14. At what rate of compound interest per annum will a sum of Rs.1200 become Rs.1348.32 in 2 years?

a) 6% b) 6.5% c)7% d) 7.5%

15. If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what is the compound interest on the same at the same rate and for the same time?

a)Rs. 52 b)Rs. 51.25 c)Rs. 54.25 d) Rs. 60

16. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

a) Rs.1550 b)Rs.1650 c) Rs.1750 d) Rs.2000

17. if the annual rate of simple interest increases from 10% to 12.5% .Then a man’s yearly income from an investment increases by Rs.1250. His principle amount is:

a) Rs,45000 b)Rs.50,000 c) Rs. 60,000 d) Rs.65,000

18. Raghav borrows Rs.2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be ?

a) Rs.1275 b) Rs.1283 c) Rs.1352 d) Rs.1377

19. A man invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest of 5% per annum. How much amount will Albert get on maturity of the fixed deposit ?

a) Rs.8600 b) Rs.8620 c) Rs.8820 d) Rs. 8840

20 . The difference between simple interest and compound interest on Rs.1200 for one year at 10% per annum reckoned half-yearly is :

a) Rs.2.50 b) Rs.3 c)Rs.3.75 d) Rs.4

**Answer & Explanations**

1. Expl: S.I. = 1680, R = 4% T = 5 years

Principal = (100 *1680)/ (5*4) = 8400

So P = 8400

Rate = (100 *1680)/ (8400 * 4) = 5%

2. Expl : S.I. = Rs. 405 R = 4.5% T = 1 year

Principal = (100 *405)/(4.5*1) = Rs.9000

S.I at 5% interest = (9000*5*1)/100 = Rs.450

Difference in interest = 450 – 405 = Rs.45

3. Let the sum invested in Scheme S1 be Rs.x and that in Scheme S2 be Rs.(13900-x).

Then, (x*14*2)/100 + ((13900-x)*11*2)/100 = 3508;

28x-22x= 3350800-(13900*22);

6x = 45000; x= 7500

So sum invested in Scheme S2 = Rs. (13900-7500) = Rs.6400

4. Let the sum be Rs.x

S.I from the bank = x*8*3/100 = 34x/100Earnings in the form of interest from mutual fund = (x * 8.5

*4)/100 = 34x/100

Given that 34x/100 - 34x/100 = Rs.500 ; x = 5000

: . The sum invested = 5000

5. Let the time be x years. Then (600 *3* x)/100 + (800*9*x)/(2*100) = 24

18x+ 36x = 246 ; x = 246/54 = 4 years

Required time = 4 years

6. Let the amounts be x, y, z in ascending order of value. As the interest rate and interest accrued are

same for 4 years 3 years and 2 years i.e. 4x = 3y = 2z = k.

L.C.M. of 4,3,2 = 12 So x:y:z: = 3000 : 4000 :6000

The amount deposited for 4 years = 3000

7. Total amount of Interest is

I = P/100 * 1[3/12 + 9/12 +27/12…. 3^{12}/12

Where P = 100; I = 1/12 (3+9+…..3^{12})

I = 1/12(3(3^{12}-1))/3-1

= 531440* 3/12*2 =Rs.66430

8. Expl: S I for 2 years = 3800 ie for one year =1900

The compound interest for Rs.1900 for the second year = 1900*12/100 =228

The CI for two years 3800+228 = 4028

9. Principal = 882/(1+(5/100)) + 882/(1+(5/100)= (882*20)/21+ (882*400)/441

=840 +800 = Rs.1640

10. Expl : Option (a). Let the second amount be Rs.x. then,

(12000* 10 * 1)/100 + (x*20 *1)/100 = ((12000 +x)* 14*1)/100

= 1200 +x/5 = (168000 +14x)/100

600000 + 100x = 840000 +70 x

30x = 240000; X = 8000

Total investment = 12000 +8000 = Rs.20000

11. Let the savings be X and Y and the rates of simple interest be 4x and 5x respectively.

Then X +4x * 1/2 *1/100 = Y + 5x * 1/2 *1/100 or X/Y = 5/4 i.e. X : Y = 5 : 4

12. Expl:Let sum be Rs.100. After 16 years it become 300. With in 16 years it increased Rs.200 i.e. after 8

years it is doubled. So after 32 years interest become Rs.400. Total Rs.500 i.e. 5 times more than the

sum. So 32 years is the answer.

13. Expl: Amount = Rs. (30000 + 4347) = Rs. 34347.

Let the time be *n* years.

Then, 30000 (1 + 7/100)^{n }= 34347

(107/100) ^{n} = 34347/30000 = 11449/10000 = (107/100)2

So the period is 2 years.

14. Expl: Let the rate be R% p.a. (1+ R )^{2} = 1348.32. Then, 1200* (1+ (R/100))2 = 1348.32

(1+R/100)2 = 134832/120000 = 11236/10000 :. (1 + R/100) 2 = (106/100)2

1 + R/100 = 106/100. So R = 6%

15. Expl: Simple interest for 2 years = Rs.50 ie. For 1 years Rs. 25. . In the first year the S.I and C.I are

same ie.Rs. 25. So in the 2^{nd} year in C.I calculated for 1 years interest also. So in second years for

Rs.25 interest is 25*5/100 = 1.25 . So total C.P = 51.25.

16. Expl: C.I = 4000 * (1+10/100)^{2} –4000

= 4000 *11/10 + 11/10 –4000 = Rs.840

:. Sum = Rs.(420 * 100)/ (3 *8) = Rs.1750

17. Expl : Let the sum be Rs.x Then, (x*25/2*1/100) – (x*10*1/100)= 1250

25x-20x = 250000 ; x=50000

18. Expl : Let the value of each instalment be Rs.x.

x/(1+4/100) + x/(1+4/100)^{2} = 2550 = 25x/26 + 625x/676 = 2550

1275x = 2550 *676

x = (2550*676)/1275 = 1352.

:. Value of each instalment = Rs.1352

19. Expl : Amount = 8000 *1+(5/100)^{2} = 8000 *21/20 * 21/20 = Rs.8820

20. Expl : S.I = (1000 *10 *4)/100 = Rs.400

C .I =1200 *1+5/100)2 –1200 = 123.

Difference = Rs.(123-120) = Rs.3

Simple interest and compound interest problems are very important in all entrance exams. When a person or bank lends money to a borrower, the borrower usually has to pay an extra amount of money to the lender. This extra money is called interest. Simple interest is based on the principal amount of a loan or deposit, while compound interest is the interest that is added to the principal at the end of the each period to arrive at the new principal for the next period. Under compound interest, the amount at the end of the first year will become principal for the second year; the amount at the end of the second year becomes the principal for the third year and so on.
Freshersworld.com explains basic concept of simple and compound interest and provides aptitude test tricks, shortcuts and formulas. It also provides questions and answers, Problems with Solutions on simple and compound interest.
What is the formula for simple and compound interest?
Simple interest formula =P*R*T
Compound interest formula
A=P(1r/n)nt
What is the difference between simple interest and compound interest?
Simple Interest refers to an interest that is calculated as a percentage of the principal amount, whereas Compound Interest refers to an interest which is calculated as a percentage of principal and accrued interest. Principal remains constant while calculating interest according to simple interest but principal changes during the entire borrowing period while calculating interest according to compound interest.