**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Interest (Simple & Compound)**

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If someone borrows some money for a particular time period from some other person or firm, then he pays back some additional amount of money with the borrowed money. The additional amount of money paid is called interest.

**Fundamental Definitions**

Some important definitions related to simple interest are as given below

**Principal (P)** The sum of money which we borrow from banks or institutions is termed as principal.

**Rate of interest (R)** This is the rate on which the extra money what we pay for keeping or using of money is calculated. It is in per cent form.

e.g., 20% rate of interest means for every hundred rupees, we have to pay Rs 20 each year.

**Amount (A)** Total money what we return to the bank after end of period is called amount. In other words, amount is the sum of principal and interest accrued on principal.

i.e., Amount = Principal + Interest

**Time (t)** The period, for which the money is lent or deposited or borrowed, is called time. There are two ways of calculating interest

1. Simple Interest

2. Compound Interest

**Simple Interest .**

If the interest in calculated on the original principal at any rate of interest for any period of time, then it is called simple interest.

**Example What rate give Rs 280 as interest on a sum of Rs 56000 in 2 yr?**

(a) 0.15%

(b) 0.25%

(c) 0.35%

(d) 0.45%

**Example A person invests Rs 12000 as fixed deposit at a bank at the rate of 10% per annum simple interest. But due to some pressing needs he has to withdraw the entire money after 3 yr for which the bank allowed him a lower rate of interest. If he gets Rs 3320 less than what he would have got at the end of 5 yr, the rate of interest allowed by the bank is ssc (1o+2) 2012**

(a) 7 8/9 %

(b) 8 7/9%

(c) 7 5/9%

(d) 7 4/9 %

**Some Useful Facts/Formulae**

- If a sum of money becomes n times in T yr at simple interest, then formula for calculating interest will be given as R=100(n-1)T

**Example A sum of money becomes four times in 20 yr at SL Find the rate of interest.**

(a) 12%

(b) 15%

(c) 14.5%

(d) 16%

- If SI for a certain sum P1 for time T1 and rate of interest R1 is I1 and SI for another sum P2 for time T2 and rate of interest is then,

Difference of SI I2 – I1 =P2R2T2-P1R1T1/100

**Example Simple interest for a sum of Rs 1550 for 2 yr is Rs 20 more than the simple interest for Rs 1450 for the same duration. Find the rate of interest.**

(a) 12%

(b) 11%

(c) 10.5%

(d) 10%

- The annual payment that will discharge a debt of Rs P due in T yr at the rate of interest R% per annum is

**Example What annual payment will discharge a debt of Rs 6450 due in 4 yr at 5% per annum simple interest? SSC (10 + 2) 2010**

(a)Rs 1400

(b)Rs 1500

(c)Rs 1550

(d)Rs 1600

**Compound Interest**

In compound interest principal is not constant for the whole time period as it is in simple interest. For the calculation of compound interest, the amount (Principal + Interest) calculated for the first year on given principal, is taken as principal for the second year and the amount (Principal + Interest) calculated for second year is considered as principal for the third year and this process keeps going on for the stipulated time.

=> SI for the first year on a principal = CI for the first year on the same principal,

**Example The compound interest on Rs 30000 at 7% per annum for a certain time is Rs 4347. The time is SSC (10 + 2) 2012**

(a) 2 yr

(b) 2.5 yr

(c) 3 yr

(d) 4yr

**Example A sum of money at compound interest doubles itself in 15 yr. It will become eight times of itself in ssc (10+2) 2010**

(a) 45 yr

(b) 48 yr

(c) 54 yr

(d) 60 yr

**Some Useful Facts/Formulae**

- When interest is not compound annually

Where, n = number of compounding per year

i.e., n = 2, if compounded half-yearly

n = 4, if compounded quarterly

**Example Calculate the compound interest for the money Rs 840, if the rate is 20% compounded on half-yearly basis for 2 yr. (a) Rs 390**

(b) Rs 400

(c) Rs 490

(d) Rs 380

- If the population of a city is P and it increases with the rate of R% pa, then

**Example The population of a city increases at the rate of 15% pa. If its population was 4000 at the end of year 2009, what will be its population at the end of year 2011?**

(a) 5290

(b) 5390

(c) 5120

(d) 5250

- Calculation of installment when interest is compounded.

Let the borrowed amount = Rs P

Rate of interest compounded annually = R

Amount of each installment = Rs a and time =t yr

**Example If the difference between simple interest and compound interest on a certain sum of money for 3 yr at 10% per annum is Rs 31, the sum is SSC (1o+2) 2011**

(a)Rs 500

(b)Rs 750

(c)Rs 1000

(d)Rs 1250

**Reference Corner**

**1.A bank offers 5% compound interest per half year. A customer deposits Rs 9600 each on January 1 and July 1 of a year. At the end of the year, the amount he would have gained by way of interest is SSC (10 + 2) 2017**

(a) Rs 2928

(b) Rs 1464

(c) Rs 732

(d) Rs 366

**2.On what sum of money will the difference between simple interest and compound interest for 2 yr at 5% per annum be equal to Rs 63? SSC (10 + 2) 2015**

(a)Rs 24600

(b)Rs 24800

(c)Rs 25200

(d)Rs 25500

**3. The compound interest on a sum of money for 2 yr is Rs 615 and the simple interest for the same period is Rs 600. Find the principal. SSC (10+2) 2014**

(a) Rs 8000

(b) Rs 9500

(c) Rs 6500

(d) Rs 6000

**4. The population of a village increases by 5% annually. If its present population is 4410, then its population 2 yr ago was SSC (10 + 2) 2014**

(a) 4500

(b) 4000

(c) 3800

(d) 3500

**5.A sum of Rs 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment is SSC (10+2) 2014**

(a) Rs 127

(b) Rs 121

(c) Rs 210

(d) Rs 225

**6.If x, y, z Eire three sums of money such that y is the simple interest on x and z is the simple interest on y for the same time and at the same rate of interest, then we have SSC (10 + 2) 2013**

(a)x² = yz

(b)y²=zx

(c)z² =xy

(d) xyz = 1

**7.The simple interest at x% for z years will be Rs x on a sum of SSC (10 + 2) 2013**

(a) Rs x

(b) Rs 100x

(c) Rs 100/x

(d) Rs 100/x²

**Practice Exercise**

**1. A certain sum of money lent at simple interest amount to Rs 616 in 3 yr and to Rs 700 in 5 yr. Find the rate per cent.**

(a)4

(b)5

(c)6

(d)6 1/4

**2. The difference between simple interest of 12% per annum and compound interest of 12% per annum compounded half yearly on a sum of Rs 3000 in one year is**

(a) Rs 10.80

(b) Rs 12.00

(c) Rs 18.00

(d) Rs 24.00

**3. If a sum of money at a certain rate of simple interest doubles in 5 yr and at a different rate of interest becomes three times in 12 yr, the better rate of interest is**

(a) 15%

(b) 20%

(c) 25%

(d)16 2/3%

**4. A sum of money at compound interest amounts to Rs 578.40 in 2 yr and to Rs 614.55 in 3 yr. The rate of interest per annum is**

(a) 4%

(b) 5%

(c) 6 1/4%

(d) 8 1/3%

**5. a, b and c are three sums of money such that b is simple interest on a, b is simple interest on c for the same time and same-rate of interest. Then, we have**

(a) a² = bc

(b) b² = ac

(c) c² =ab

(d) abc =1

**6. The difference in simple and compound interest on a certain sum of money in 2 yr at 15% per annum is Rs 144. The sum is**

(a) Rs 6000

(b) Rs 6200

(c) Rs 630.0

(d) Rs 6400

**7. A certain sum of money at simple interest amounts to Rs 1260 in 2 yr and to Rs 1350 in 5 yr. The rate per cent per annum is**

(a) 2.5

(b) 3.75

(c) 5.0

(d) 7.5

**8. The difference between simple and compound interest on a sum of money at 5% per annum for 2 yr in Rs 25. The sum is**

(a)Rs 1000

(b)Rs 5000

(c)Rs 10000

(d)Rs 11000

**9. A certain sum of money at simple interest amounts to Rs 1300 in 4 yr and to Rs 1525 in 7 yr. The rate per cent per annum is**

(a) 6 1/2

(b) 8

(c) 8 1/2

(d)7 1/2

**10. A certain sum of money lent out at simple interest amounts Rs 500 in 3 yr and Rs 750 in 5 yr. The sum lent is**

(a) Rs 400

(b) Rs 450

(c) Rs 500

(d) Rs 60

**11. A man is given Rs 1200 for 5 yr at a special rate and Rs 1500 for 3 yr at the same rate of interest. If the total simple interest is Rs 315. Find the rate of interest.**

(a) 2%

(b) 3%

(c) 5%

(d) 7%

**12.Divide Rs 2602 between X and Y, so that the amount of X after 7 yr is equal to the amount of Y after 9 yr, the interest being compounded at 4% per annum.**

(a) Rs 1352, Rs 1250

(b) Rs 1400,Rs 1350

(c) Rs 1415, Rs 1300

(d) Rs 1500,Rs 1450

**13. Sagar had Rs 10000 with her. Out of this money, she lent some money to Akshay for 2 yr at 15% simple interest. She lent remaining money to Brijesh for an equal number of years at the rate of 18%. After 2 yr Sagar found that Akshay had given her Rs 360 more as interest as compared to Brijesh. The amount of money which Sagar had lent to Brijesh must be**

(a) Rs 4000

(b) Rs 2500

(c) Rs 3500

(d) Rs 4200

**14. Rachana borrowed Rs 500 at 3% per annum simple interest and Rs 600 at % per annum simple interest on the agreement that the whole sum will be returned only when the total interest becomes Rs 252. The number of years after which the borrowed sum is to be returned, is**

(a) 8 yr

(b) 5 yr

(c) 7 yr

(d) None of these

**15. The difference between the simple interest and the compound interest (Compounded annually) at the rate of 12% per annum on Rs 5000 for 2 yr will be**

(a) Rs 17.50

(b) Rs 36

(c) Rs 45

(d) Rs 72

**16. Compound interest (compounded annually on) a certain sum of money for 2 yr at 4% per annum is Rs 102. The simple interest on the same sum for the same rate and for the same period will be**

(a) Rs 99

(b) Rs 101

(c) Rs 100

(d) Rs 98

**17. A builder borrows Rs 2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 yr in two equal yearly instalments. How much will each, instalment be? **

(a) Rs 1352

(b) Rs 1377

(c) Rs 1275

(d) Rs 1283

**18. The compound interest on a certain sum for 2 yr is Rs 618 whereas the simple interest on the same sum at the same rate for 2 yr is Rs 600. The rate of interest per annum is**

(a) 18%

(b) 9%

(c) 6%

(d) 3%

**19. Two equal sum of money were invested, one at the rate 4 % and the other at the rate 4 1/2%. At the end of 7 yr, the simple interest received from the former by Rs 31.50. Each sum was**

(a) Rs 1000

(b) Rs 500

(c) Rs 750

(d) Rs 900

**20. If the difference between the compound interest, compounded every 6 months and the simple interest on a certain sum of money at the rate of 12% per annum for 1 yr is Rs 36. The sum is**

(a)Rs 10000

(b)Rs 12000

(c)Rs 15000

(d)Rs 9000

**Answers**

**Hints & Solutions**

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