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

Answer: Option C

Explanation:

\begin{aligned}
S.I. = \frac{P*R*T}{100} \\
P = \frac{50*100}{5*2} = 500\\

Amount = 500(1+\frac{5}{100})^2 \\
500(\frac{21}{20} * \frac{21}{20}) \\
= 551.25 \\

C.I. = 551.25 - 500 = 51.25


\end{aligned}

Answer: Option C

Explanation:

Please remember, when we have to calculate C.I. quarterly then we apply following formula if n is the number of years

\begin{aligned}
Amount = P(1+\frac{\frac{R}{4}}{100})^{4n}
\end{aligned}

Principal = Rs.16,000;
Time=9 months = 3 quarters;
Rate = 20%, it will be 20/4 = 5%

So lets solve this question now,

\begin{aligned}
Amount = 16000(1+\frac{5}{100})^3 \\
= 18522\\
C.I = 18522 - 16000 = 2522
\end{aligned}

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

Answer: Option B

Explanation:

\begin{aligned}
Amount = [7500 \times (1+ \frac{4}{100})^2] \\
= (7500 \times \frac{26}{25} \times \frac{26}{25}) \\
= 8112 \\

\end{aligned}

So compound interest = (8112 - 7500) = 612

Answer: Option A

Explanation:

Let the amount Rs 100 for 1 year when compounded half yearly, n = 2, Rate = 6/2 = 3%

\begin{aligned}
Amount = 100(1+\frac{3}{100})^2 = 106.09
\end{aligned}

Effective rate = (106.09 - 100)% = 6.09%