The present worth of Rs.169 due in 2 years at 4% per annum compound interest is

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:

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

So compound interest = (8112 - 7500) = 612

Answer: Option A

Explanation:

As per question we need something like following

$$\begin{aligned} P(1+\frac{R}{100})^n > 2P \\ (1+\frac{20}{100})^n > 2 \\ (\frac{6}{5})^n > 2 \\ \frac{6}{5} \times \frac{6}{5} \times \frac{6}{5}\times\frac{6}{5} > 2 \end{aligned}$$

So answer is 4 years

Answer: Option D

Explanation:

Let Rate will be R%

$$\begin{aligned} 1200(1+\frac{R}{100})^2 = \frac{134832}{100} \\ (1+\frac{R}{100})^2 = \frac{134832}{120000} \\ (1+\frac{R}{100})^2 = \frac{11236}{10000} \\ (1+\frac{R}{100}) = \frac{106}{100} \\ => R = 6\% \end{aligned}$$

Answer: Option C

Explanation:

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