Effective annual rate of interest corresponding to nominal rate of 6% per annum compounded half yearly will be

Answer: Option A

Explanation:

$$\begin{aligned} (25000 \times (1 + \frac{12}{100})^3) \\ => 25000\times\frac{28}{25}\times\frac{28}{25}\times\frac{28}{25} \\ => 35123.20 \\ \end{aligned}$$

So Compound interest will be 35123.20 - 25000
= Rs 10123.20

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:

S.I. on Rs 800 for 1 year = 40

Rate = (100*40)/(800*1) = 5%

Answer: Option C

Explanation:

$$\begin{aligned} [200(1+\frac{5}{100})^3 + 200(1+\frac{5}{100})^2+ \\ 200(1+\frac{5}{100})] = [200(\frac{21}{20} \times \frac{21}{20} \times \frac{21}{20})\\ + 200(\frac{21}{20}\times\frac{21}{20})+200(\frac{21}{20})] \\ = 662.02 \end{aligned}$$

Answer: Option B

Explanation:

$$\begin{aligned} C.I. = (4000 \times(1+\frac{10}{100})^2 - 4000) \\ = 4000 * \frac{11}{10} * \frac{11}{10} - 4000 \\ = 840 \\ \text{So S.I. = } \frac{840}{2} = 420\\ \text{So Sum = } \frac{S.I. * 100}{R*T} \\ = \frac{420 * 100}{3*8} \\ = Rs 1750 \end{aligned}$$