# 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:

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

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

$=&space;25000\left&space;[&space;\frac{112}{100}&space;\right&space;]^3&space;-&space;25000$

$=&space;25000&space;\left&space;[&space;\frac{28}{25}&space;\right&space;]&space;^3&space;-&space;25000$

$=&space;25000\left&space;[&space;\frac{28}{25}&space;\times&space;\frac{28}{25}&space;\times&space;\frac{28}{25}\right&space;]&space;-&space;25000$

$=&space;10123.20$

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:

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

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

$=&space;8000\left&space;[&space;\frac{105}{100}&space;\right&space;]^2$

$=&space;8000\left&space;[&space;\frac{21}{20}&space;\right&space;]^2$

$=&space;8000\left&space;[&space;\frac{21}{20}&space;\times&space;\frac{21}{20}\right&space;]$

$=&space;8820$

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:

$\text{If&space;interest&space;is&space;compounded&space;half-yearly}$

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

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

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

$=&space;15000\left&space;[&space;\frac{105}{100}&space;\right&space;]^2$

$=&space;15000\left&space;[&space;\frac{21}{20}&space;\right&space;]^2$

$=&space;15000\left&space;[&space;\frac{21}{20}&space;\times&space;\frac{21}{20}\right&space;]$

$=&space;16537.50$

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:

$\text{Let&space;the&space;time&space;be&space;T&space;years,&space;then}$

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

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

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

$\left&space;[&space;\frac{11}{10}&space;\right&space;]^\text{T}&space;=&space;\left&space;[&space;\frac{11}{10}&space;\right&space;]^3$

$\therefore&space;\text{3&space;years}$

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:

$\text{Let&space;the&space;sum&space;be&space;Rs.}x$

$\text{C.I.&space;-&space;S.I.}&space;=&space;631$

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

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

$\left&space;[&space;\frac{121x}{100}&space;-&space;x\right&space;]&space;-&space;\left&space;[&space;\frac{x}{5}&space;\right&space;]&space;=&space;631$

$\left&space;[&space;\frac{21x}{100}&space;\right&space;]&space;-&space;\left&space;[&space;\frac{x}{5}&space;\right&space;]&space;=&space;631$

$\frac{x}{100}&space;=&space;631$

$x&space;=&space;63100$

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:

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

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