Principal: – The money borrowed or lent out for certain period is called the principal or the Sum.

Interest: – Extra money paid for using other money is called interest.

If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest.

Let Principal = P, Rate = r % per annum (p.a.), and Time = t years then

Simple Interest(SI)= ((P×r×t))/100

Using this formula we can also find out

P=(100×SI)/(r×t);

r=(100×SI)/(P×t);

t=(100×SI)/(P×r).

**Compound Interest:**

When compound interest is applied, interest is paid on both the original principal and on earned interest.

So for one year Simple interest and Compound interest both are equal.

Suppose if you make a deposit into a bank account that pays compounded interest, you will receive interest payments on the original amount

that you deposited, as well as additional interest payments.

This allows your investment to grow even more than if you were paid only simple interest.

So Amount at the end of 1st year (or Period) will become the principal for the 2nd year (or Period) and

Amount at the end of 2nd year (or Period) becomes the Principal of 3rd year.

Amount = Principal + Interest

A= P (1+r/100) ^n

A= Amount,

P= Principal,

r= Rate %,

n= no. of years.

So Compound Interest = [P (1+r/100) ^ n – P]

= P [(1+r/100) ^ n – 1]

**Condition:-**

**1.**When interest is compounded annually,

Amount = P(1+r/100)^n

**2.**When interest is compounded half yearly,

Amount = P(1+(r/2)/100)^2n

**3.**When interest is compounded Quarterly,

Amount =P(1+(r/4)/100)^4n

**4.**When interest is compounded annually but time is in fraction, say 3 whole 2/5 year

Amount = P(1+r/100)^3×(1+(2r/5)/100)

**5.**When Rates are different for different years, say r1%, r2%, and r3% for 1st, 2nd and 3rd year respectively.

Then,

Amount = P(1+r1/100)×(1+r2/100)×(1+r3/100).

Present worth of Rs. x due n years hence is given by:

Present Worth = x/(1+r/100)

**Difference between Compound Interest & Simple interest Concept For Two years**

CI – SI =P(r/100)^2

For Three Year

CI – SI =P(r^2/(100^2 ))×(300+r)/100)

For Two year

**CI/SI=(200+r)/200**

**Quant Quiz for Simple Interest & Compound Interest**

**1. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:**

A) Rs. 720

B) Rs. 698

C) Rs. 678

D) Rs. 696

E) none of these

**2. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 % p.a. in 5 years. What is the sum?**

A) Rs. 8045

B) Rs. 8925

C) Rs. 8900

D) Rs. 8032.45

E) none of these

**3. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest.**

**The rate of interest per annum is:**

A) 12 %

B) 13 %

C) 8 %

D) 12.5 %

**4. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6.25% p.a. for 2 years.**

**Find his gain in the transaction per year.**

A) Rs. 112.50

B) Rs. 175

C) Rs. 150

D) Rs. 125.50

**5. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period.**

**The principal amount borrowed by him was**:

A) Rs. 12000

B) Rs.15000

C) Rs. 12500

D) Rs. 22000

**6.How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?**

A)3 year

B)4 year

C)5 year

D)6 year

**7. Bhavika took a loan of Rs. 1200 with simple interest for as many years as the rate of interest.**

**If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?**

A)3.6

B) 5

C) 6

D)25

**8. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:**

A) 5 %

B) 7%

C)10 %

D) 12%

9.

**A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year.****At the end of the year, the amount he would have gained by way of interest is:**

A)123

B) 122

C)121

D)120

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

A)2.5

B) 2

C) 3

D) 4

E) none of these

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

A)8 %

B) 9%

C) 6 %

D) 8.5 %

E) none of these

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

A)Rs. 3

B) Rs. 4

C) Rs. 3.5

D) Rs. 7.5

E) none of these

**13.The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:**

A) 4

B) 5

C) 6

D) 2.5

E) none of these

**14.What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?**

A) Rs.10123.20

B) Rs. 9000

C) Rs. 12000

D) Rs. 10163.34

E) none of these

**15.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. 1650

B)Rs. 2000

C)Rs. 1750

D) Rs.1550

E) none of these

**Answers with Explanation:**

Anwers:

1.B

2.B

3.A

4.A

5.B

6.B

7.C

8.C

9.C

10.B

11.C

12.A

13.A

14.A

15.C

Explanation

1.S.I. for 1 year = Rs. (854 – 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

Principal = Rs. (815 – 117) = Rs. 698.

2.Sum = (100× S.I.)/ r × t

= (100 × 4016.25)/ 9 × 5 = Rs. 8925

3.S.I. for 3 years = Rs. (12005 – 9800) = Rs. 2205.

S.I. for 5 years= Rs. 3675

Principal = Rs. (9800 – 3675) = Rs. 6125

Hence Rate = {(100 × 3675) / 6125 × 5} % = 12 %

4.Gain in 2 years = Rs. [{(5000×6.25×2)/100} – {(5000×4×2)/100}]

= Rs. (625- 400) = Rs. 225.

So gain in 1 year = Rs.225/ 2 = Rs. 112.50

5.Principal = Rs. {(100× 5400)/ (12×3)} = Rs.15000.

6.Time =(100×81)/ (450×4.5) years = 4 years

7.Let rate = r% and time = r years

Then (1200×r×r)/100= 432

12 r^2= 432

r=6 %

8.Let the rate be r% p.a.

Then,(5000 x r x 2)/100 +(3000 x r x 4)/100 = 2200.

100R + 120R = 2200

R = 2200/220= 10.

Rate = 10%.

9.Amount = Rs. [1600×(1+ 5/200)^2 + 1600 × (1+5/200)]

= Rs. 3321

So CI = Amount- Principal

= Rs. 3321 – Rs. 3200 = Rs. 121

10.Amount = Rs. (30000 + 4347) = Rs. 34347,

Let the time be n years then

30000(1+7/100) ^n = 34347

(107/100) ^n = 34347/30000

So n= 2 year.

11.Let rate r % per annum

1200× (1+r/100) ^ 2 = 1348.32

(1+r/100) ^ 2 = 1348.32/1200

1+r/100 = 106 / 100

r= 6 %

12.SI =Rs. (1200 ×10×1)/100= Rs. 120

CI = Rs.[ 1200×(1+5/100) ^2 – 1200] = Rs.123

So CI-SI = Rs. 3

13.P(1+20/100) ^n > 2P

(6/5)^ n >2

(6/5×6/5×6/5×6/5)>2

so n = 4 years

14.Amount= Rs. 25000(1+12/100)^3= 35123.20

So CI= Rs. (35123.20 – 25000) = Rs. 10123.20

15.C.I.= Rs. 4000(1+10/100)^2 – 40

= Rs. 840

Sum= Rs. (420 × 100)/(3×8) = Rs. 1750