Find the compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.

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 C

Explanation:

$$\begin{aligned} S.I. = \frac{1000*10*4}{100} = 400 \\ C.I. = [1000(1+\frac{10}{100})^4 - 1000] \\ = 464.10 \end{aligned}$$

So difference between simple interest and compound interest will be 464.10 - 400 = 64.10

Answer: Option B

Explanation:

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

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

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%

Answer: Option D

Explanation:

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