8
Q:

# Rs 1000 is being  charged at 50% per annum. what is the interest for 3rd year at compound interest?

 A) 1122 B) 1025 C) 1125 D) 625

Explanation:

Total amount for two years = $\inline&space;1000(1.5)^2=2250$

Now , interest for third year = $\inline&space;\frac{2250\times&space;50\times&space;1}{100}=1125$

Q:

Sonika invested an amount of Rs.5800 for 2 years. At what rate of compound interest will she get an amount of Rs.594.50 at the end of 2 years ?

 A) 6.5% B) 6% C) 5% D) 4.5%

Explanation:

C.I = $\inline \fn_jvn \small P\left [ \left ( 1+\frac{r}{100} \right )^{t}-1 \right ]$

594.5 = $\inline \fn_jvn \small 5800\left [ \left ( 1+\frac{r}{100} \right )^{2} -1\right ]$

$\inline \fn_jvn \small \frac{594.5}{5800}+1=\left ( 1+\frac{r}{100} \right )^{2}$

$\inline \fn_jvn \small \frac{r}{100}=1.05-1=0.05\Rightarrow r=5$ % .

3 112
Q:

The compound interest on a certain sum for 2 years at 10% per annum is Rs. 1155. The simple interest on the same sum for double the time at half the rate percent per annum is ?

 A) Rs. 1100 B) Rs. 5500 C) Rs. 1400 D) Rs. 4120

Explanation:

Let the sum be Rs.x. Then,

$\inline \fn_jvn \small \left [ x\left ( 1+\frac{10}{100} \right )^{2}-x \right ]=1155$

$\inline \fn_jvn \small \Rightarrow x\left [\left ( \frac{11}{10} \right )^{2}-1 \right ]=1155$

=> x =5500

sum = Rs. 5500.

So, S.I = Rs. $\inline \fn_jvn \small \left ( \frac{5500x5x4}{100} \right )=Rs. 1100$

2 213
Q:

There is 50% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate ?

 A) Rs. 5422 B) Rs. 5489 C) Rs. 3972 D) Rs. 6145

Explanation:

Let p = Rs. 100.
Then, S.I is Rs. 50 and time = 5 years.

$\inline \fn_jvn \small \therefore R=\frac{100\times 50}{100\times 5}$ = 10% p.a.

Now, p = Rs. 12,000 , T = 3 years and R = 10% p.a.
C.I. = Rs. $\inline \fn_jvn \small \left [ 12000\times \left \{ \left ( 1+\frac{10}{100} \right )^{3}-1 \right \} \right ]$= Rs. $\inline \fn_jvn \small \left ( 12000\times \frac{331}{1000} \right )=Rs. 3972.$

4 211
Q:

The minimum number of half years in which a sum of money kept at 60% compound interest will be quadrupled is ?

 A) 2 B) 4 C) 3 D) 6

Explanation:

Let us assume Amount be 100 Rs and we calculate in CI

First year 60% of 100 = 60 amount (100+60) is 160

Second year 60% of 160 = 96 amount (160+96) is 256

Third year 60% of 256 =153.6 amount (256+153.6) is 409.6

Here the Amount of 100 Rs is quadrapled in 3 years.

One year contains 2 half years

Three year has 6 half years.

$\inline \fn_jvn \small \therefore$ It takes 6 half years.

10 317
Q:

A certain sum is to be divided between A and B so that after 5 years the amount received by A is equal to the amount received by B after 7 years. The rate of interest is 10%, interest compounded annually. Find the ratio of amounts invested by them.

Let the sum(principal) received by A and B are x and y.

(1+r) = $\inline \fn_jvn 1+\frac{1}{10}$ =$\inline \fn_jvn \frac{11}{10}$

Then, $\inline \fn_jvn \frac{x}{y}=\left ( \frac{11}{10} \right )^{7-5}$ =$\inline \fn_jvn \left ( \frac{11}{10} \right )^2 =\frac{121}{100}$

Hence, the ratio in which the sum is divided =121:100