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SIMPLE AND COMPOUND INTEREST★ Interest is the money that paid for the use of

a certain amount.★ The amount borrowed is called the Principal. ★ The sum of interest and principal is called

the Amount.

SIMPLE INTERESTIf the interest is calculated on original

Principal for a certain period is called theSimple Interest (S.I.). Simple Interest will be thesame for all the years.

If P is the principal, R is the rate of interest,T is the time and S.I. the simple interest, then

PTRSimple Interest = ⎯⎯

100TR

Amount = P (1+ ⎯⎯)100e.g: Find the Simple Interest obtained on an

amount of Rs.16800 at the rate of 4 1⎯2

p.c.p.a. for a period of 3 years

Sol: Here P = Rs.16800, T = 3 years

R = 4 1⎯2

% = 9⎯2

%

16800 × 3 × 9 Simple Interest = ⎯⎯ = Rs. 2268

2 × 100

e.g: What principal will amount to Rs.5700 at

4% per annum in 3 1⎯2

years?

TRSol: Amount = P(1 + ⎯⎯)100

7 × 4⇒ P (1 + ⎯⎯ ) = 5700

2 × 100

5700 × 2 × 100⇒ P = ⎯⎯⎯ = Rs. 5000

228Shortcut: For one year, rate of interest is 4%

and for 3 1⎯2

years it is 4 × 3 1⎯2

= 14%

The amount will become 114%.If 114% money = 5700,

100then 100% money = ⎯ × 5700

114

= Rs. 5000

COMPOUND INTEREST

When the interest that has become due atthe end of a period is not paid to the lender, butis added to the sum lent which then becomes

the principal for the next period, then the moneyis said to be lent at Compound Interest. Thusthe amount at the end of period becomes theprincipal for the next period.

If A is the amount, C.I. is the CompoundInterest, P is the principal, R is the rate, and Tis the time, then

R TA = P [1+ ⎯ ]100

R TC.I. = P [1 + ⎯ ] − P

100e.g: What is the Compound Interest accrued on

an amount of Rs. 8000 at the rate of 5 p.c.p.a. at the end of 3 years?

R TSol: C.I. = P [1 + ⎯ ] − P

100

5 3C.I. = 8000 [1 + ⎯ ] − 8000

100

105 105 105⇒ [8000 × ⎯ × ⎯ × ⎯ ] − 8000

100 100 100

= Rs.1261

Shortcut: Amount = 105% of 105%of 105% of 8000 = Rs. 9261

∴ C.I. = 9261 − 8000 = Rs.1261Note: ★ If the Interest is paid half yearly, time

is doubled and the rate is halved.★ If the Interest is paid quarterly, time

becomes 4 times and the rate becomesone -fourth

Difference between Simple and Compound Interest

It can be calculated by the following formulae.★ For one year: There is no difference.

P × R2★ For 2 years: Difference = ⎯⎯

1002

(300 + R) P × R2

★ For 3 years: Difference = ⎯⎯⎯⎯1003

If the rate of interests are 5% and 10%, thefollowing formulae can be used @ 5%

Difference 61

= P × ⎯8000

@ 10% Difference =31

P × ⎯1000

e.g: What is the differ-ence betweenSimple and Compound Interest onRs.42800 for two years at 5% rate?

P × R2 42800 × 25Difference = ⎯⎯⇒ ⎯⎯ = Rs.107

1002 10000e.g: On what sum does the difference between

Simple and Compound Interest for 3 yearsat 10% rate will be Rs.403?

P × 31 P × 31Sol: Difference = ⎯ ⇒ 403 = ⎯

1000 1000403 × 1000

⇒ P = ⎯⎯ Rs. 1300031

1. A certain sum of money becomes Rs.1250

in a span of 5 years and further toRs.1700 in the span of 8 years at thesame rate of Simple Interest. Whatwould be the amount at the end of 12years?Sol: Interest for 3 years (8 - 5 years)

= 1700 - 1250 = Rs.4505 Interest for 5 years = — × 450 3

= Rs.750Principal = 1250 - 750 = Rs.500

12 Interest for 12 years = — × 450 = Rs.18003

∴ Amount after 12 years = 500 + 1800

= Rs.23002. An amount of Rs.15600 is to be divided into

two parts such that the Simple Interest onthe first part at 8% p.a. for 3 years is equal tothe Simple Interest on the second part at 6%p.a. for 4 years. What is the differencebetween the two parts?

Sol: Let the first part be Rs.x and 2nd will beRs.(15600 - x)x × 8 × 3 (15600 - x) × 6 × 4 ⎯⎯⎯⎯ = ⎯⎯⎯⎯

100 1002x = 15600

15600 ⇒ x = ⎯⎯⎯⎯ = Rs.7800

2Both parts are equal so there is no difference

Short cut: If we can observe 8% for 3 years on1st part is 24% and 6% for 4 years on 2nd partis also 24%. Interest on both parts are equalmeans both 1st and 2nd parts are equal.3. A sum of money amounts to Rs.1488 in 3

years at a Simple Interest. If the rate of interest is raised by 25%, the sum amountsto Rs.1560 during the same period. Find thesum and the rate of interest.

Sol: Rs.1560 - Rs.1488 = Rs.72.25% of interest = Rs.36

100∴ 100% interest = ⎯ × 72 = Rs.288

25 The interest for 3 years = Rs.288.

∴ Principal = 1488 - 288 = Rs.1200288 × 100

∴ Rate = ⎯ = 8%1200 × 3

4. A sum of money invested at Compound Interest amounts to Rs.650 at the end of firstyear and Rs.676 at the end of second year.Find the rate of interest.

Sol: Interest in 2nd year = 676 - 650 = Rs.26As this is Compound Interest, 2nd yearinterest is calculated on1st year amount

26 ∴ Rate of interest = — × 100 = 4%650

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QUANTITATIVE APTITUDE

1. What would be the Simple Interest obtainedon an amount of Rs. 52580 at the rate of 4p.c.p.a. after 3 years?A) Rs.6209.60 B) Rs.6102.70C) Rs.6309.60 D) Rs.5986.40E) None of these

2. The Simple Interest accrued on an amountof Rs.12450 at the end of 6 years is Rs. 8964. What is the rate of interest? A) 9 B) 12 C) 14 D) 10 E) None of these

3. Find the Simple Interest on Rs.8000 at 3%per annum from August 2nd to October 14th

in the same year.A) Rs.36 B) Rs.42 C) Rs.56 D) Rs.48E) None of these

4. On what sum does the difference betweenSimple Interest and Compound Interest for3 years at 5% rate be Rs.427?A) Rs.12000 B) Rs.24000C) Rs.56000 D) Rs.32000E) None of these

5. A man deposits Rs.5600 in a bank at 5%annual interest. After 6 months he withdraws Rs.4400 together with interestand after 6 months the remaining money.

How much does he get as interest?A) Rs.140 B) Rs.210C) Rs.170 D) Rs.190 E) None

6. A sum of money will become Rs.4600 in 5years and Rs.4960 in 8 years at a certainrate of Simple Interest. Find the rate ofInterest.A) 3% B) 5% C) 8% D) 4%E) None of these

ANSWERS: 1-C; 2-B; 3-D; 4-C; 5-C; 6-A.

EXPLANATIONSS.I. × 100

2. R = ⎯⎯P × T

8964 × 100⇒ R = ⎯⎯ = 12%

12450 × 63. Time from August 2nd to October 14th

= 29 days of August + 30 days ofSeptember and 14 days of October

73= 73 days = ⎯ years

3651

= ⎯ years5

18000 × 3 × ⎯

5∴ S.I. = ⎯⎯ = Rs.48

100

P × 614. D = ⎯⎯ ⇒ P = Rs.56000

8000

5. S.I. on Rs.5600 for 6 months =

15600 × ⎯ × 5

2= ⎯⎯ = Rs.140

100

He withdrew Rs.4400 together with interest,the remaining amount

= 5600 - 4400 = Rs.1200

1S.I. on Rs.1200 at the rate of 5% for ⎯ year

2

11200 × ⎯ × 5

2= ⎯⎯ = Rs.30

100

Total interest = 140 + 30 = Rs.170

6. Amount after 5 years = Rs.4600Amount after 8 years = Rs.4960Difference = 360, which is interest for 3 years

5 Interest for 5 years = ⎯ × 360 = 600

3∴ Principal = 4600 - 600 = 4000

S.I. × 100 600 × 100 R = ⎯⎯ = ⎯⎯ = 3%.

P × T 4000 × 5

(Writer - Director, RACE Institute, Hyderabad)

How much does he get as interest?

☛

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