Question Detail

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

Answer: Option D

Explanation:

Let Rate will be R%

\begin{aligned}
1200(1+\frac{R}{100})^2 = \frac{134832}{100} \\

(1+\frac{R}{100})^2 = \frac{134832}{120000} \\

(1+\frac{R}{100})^2 = \frac{11236}{10000} \\

(1+\frac{R}{100}) = \frac{106}{100} \\
=> R = 6\%
\end{aligned}

1. We need to divide Total Sum Rs. 3364 between Ram and Sham so that Ram's share at the end of 5 years may equal to Sham's share at the end of seven years with compound interest rate at 5 percent.

1864 and 1500
1764 and 1600
1664 and 1700
1564 and 1800

Answer: Option B

Explanation:

It is clear from question that Ram's share after five years = Sham's share after seven years
Hence we can conclude following :
\begin{aligned}

\text{(Rams's present share)}\left(1 + \dfrac{5}{100}\right)^5 = \text{(Sham's present share)}\left(1 + \dfrac{5}{100}\right)^7\\
=> \dfrac{\text{(Ram's present share)}}{\text{(Sham's present share)}}= \dfrac{\left(1 + \dfrac{5}{100}\right)^7}{\left(1 + \dfrac{5}{100}\right)^5} \\ = \left(1 + \dfrac{5}{100}\right)^{(7-5)} = \left(1 + \dfrac{5}{100}\right)^2 \\ = \left(\dfrac{21}{20}\right)^2 = \dfrac{441}{400}

\end{aligned}
Ram's present share : B's present share = 441 : 400

\begin{aligned}

\text{As amount is Rs.3364, Ram's share = }3364 \times \dfrac{441}{(441+400)} \\\\
= 3364 \times \dfrac{441}{841} = 4 \times 441 = \text{ Rs. 1764}
\end{aligned}

So Sham's share is = 3364-1764 = 1600

2. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs 1. Find the sum

Rs 600
Rs 625
Rs 650
Rs 675

Answer: Option B

Explanation:

Let the Sum be P
\begin{aligned}
S.I. = \frac{P*4*2}{100} = \frac{2P}{25}\\

C.I. = P(1+\frac{4}{100})^2 - P \\

= \frac{676P}{625} - P \\
= \frac{51P}{625} \\
\text{As, C.I. - S.I = 1}\\
=> \frac{51P}{625} - \frac{2P}{25} = 1 \\
=> \frac{51P - 50P}{625} = 1 \\
P = 625
\end{aligned}

3. A man saves Rs 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.

Rs 662
Rs 662.01
Rs 662.02
Rs 662.03

Answer: Option C

Explanation:

\begin{aligned}
[200(1+\frac{5}{100})^3 + 200(1+\frac{5}{100})^2+ \\ 200(1+\frac{5}{100})]

= [200(\frac{21}{20} \times \frac{21}{20} \times \frac{21}{20})\\
+ 200(\frac{21}{20}\times\frac{21}{20})+200(\frac{21}{20})] \\

= 662.02
\end{aligned}

4. On a sum of money, simple interest for 2 years is Rs 660 and compound interest is Rs 696.30, the rate of interest being the same in both cases.

Answer: Option D

Explanation:

Difference between C.I and S.I for 2 years = 36.30
S.I. for one year = 330.
S.I. on Rs 330 for one year = 36.30

So R% = \frac{100*36.30}{330*1} = 11%

5. Albert invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit.

Rs. 8510
Rs. 8620
Rs. 8730
Rs. 8820

Answer: Option D

Explanation:

\begin{aligned}
=> (8000 \times(1+\frac{5}{100})^2) \\
=> 8000 \times \frac{21}{20}\times \frac{21}{20} \\
=> 8820
\end{aligned}