Compound Interest

1. What will be the compound interest on a sum of 25000 after 3 years at the rate of 12% per annum ?

A. Rs. 10123.20

B. Rs. 12500.75

C. Rs. 8900.90

D. Rs. 11123.15

Ans: A

Explanation:

\text {C.I.} = \text{P}\left [ 1 + \frac{\text{R}}{100} \right ]^\text{T} - \text{P}

 

 

= 25000\left [ 1+\frac{12}{100} \right ]^3 - 25000

 

 

= 25000\left [ \frac{112}{100} \right ]^3 - 25000

 

 

= 25000 \left [ \frac{28}{25} \right ] ^3 - 25000

 

 

= 25000\left [ \frac{28}{25} \times \frac{28}{25} \times \frac{28}{25}\right ] - 25000

 

 

= 10123.20

 

 

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

A. Rs. 8600

B. Rs. 8620

C. Rs. 8820

D. Rs. 8990

Ans: C

Explanation:

\text {Amount} = \text{P}\left [ 1 + \frac{\text {R}}{100} \right ]^\text{T}

 

 

= 8000\left [ 1 + \frac{5}{100} \right ]^2

 

 

= 8000\left [ \frac{105}{100} \right ]^2

 

 

= 8000\left [ \frac{21}{20} \right ]^2

 

 

= 8000\left [ \frac{21}{20} \times \frac{21}{20}\right ]

 

 

= 8820

 

3. Ram invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by him at the end of the year will be

A. Rs. 15570

B. Rs. 16537.50

C. Rs.8680.20

D. Rs. 19950.75

Ans: B

Explanation:

\text{If interest is compounded half-yearly}

 

\text {Amount} = \text{P}\left [ 1+\frac{\text{R/2}}{100} \right ]^{\text {2T}}

 

 

= 15000\left [ 1+ \frac{10/2}{100} \right ]^2

 

 

= 15000\left [ 1+\frac{5}{100} \right ]^2

 

 

= 15000\left [ \frac{105}{100} \right ]^2

 

 

= 15000\left [ \frac{21}{20} \right ]^2

 

 

= 15000\left [ \frac{21}{20} \times \frac{21}{20}\right ]

 

 

= 16537.50

 

 

4. In what time will Rs. 1000 become Rs.1331 at 10% per annum compounded annually.

A. 1 year

B. 2 years

C. 3 years

D. 4 years

Ans: C

Explanation:

\text{Let the time be T years, then}

 

1000\left [ 1+\frac{10}{100} \right ]^\text{T} = 1331

 

 

1000\left [ \frac{110}{100} \right ]^\text{T} = 1331

 

 

\left [ \frac{11}{10} \right ]^\text{T} = \frac{1331}{1000}

 

 

\left [ \frac{11}{10} \right ]^\text{T} = \left [ \frac{11}{10} \right ]^3

 

 

\therefore \text{3 years}

 

 

5. The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is 631. Find the sum.

A. Rs. 62200

B. Rs. 63500

C. Rs. 63100

D. Rs. 64750

Ans: C

Explanation:

\text{Let the sum be Rs.}x

 

\text{C.I. - S.I.} = 631

 

\left [ x\left [ 1 + \frac{10}{100} \right ]^2 - x\right ] - \left [ \frac{x \times 10\times 2}{100} \right ] = 631

 

 

\left [ x\left [ \frac{11}{10} \right ]^2 - x\right ] - \left [ \frac{x}{5} \right ] = 631

 

 

\left [ \frac{121x}{100} - x\right ] - \left [ \frac{x}{5} \right ] = 631

 

 

\left [ \frac{21x}{100} \right ] - \left [ \frac{x}{5} \right ] = 631

 

 

\frac{x}{100} = 631

 

 

x = 63100

 

 

6. Find compound interest on Rs. 7500 at 4% per annum for 2 years compounded annually.

A. Rs. 590

B. Rs. 612

C. Rs. 620

D. Rs. 700

Ans: B

Explanation:

\text{Amount = Rs.}\left [ 7500 \times \left ( 1 + \frac{4}{100} \right )^2 \right ] = \text{Rs.} \left [ 7500 \times \frac{26}{25} \times \frac{26}{25}\right ] = \text{Rs.} \, 8112

 

 

\text{C.I.} = \text{Rs.} \left ( 8112 - 7500 \right ) = \text{Rs.} \, 612