Institution: Bangladesh Bank Exam: Officer (Cash) -Sonali Bank | BD Development | BD Krishi Bank - 12.10.2018 ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, we first need to determine the principal amount (P) given that the simple interest (SI) earned in 6 years is Tk. 6000 at a rate of 5% per annum.

The formula for simple interest is:
\[ \text{SI} = \frac{P \times r \times t}{100} \]
where:
- SI = Simple Interest
- P = Principal
- r = Rate of interest per annum
- t = Time in years

Plugging in the values we know:
\[ 6000 = \frac{P \times 5 \times 6}{100} \]
\[ 6000 = \frac{30P}{100} \]
\[ 6000 = 0.3P \]
\[ P = \frac{6000}{0.3} = 20000 \]

Now that we have the principal amount (P = Tk. 20000), we can calculate the compound interest (CI) for 2 years at the same rate of 5%.

The formula for compound interest is:
\[ \text{CI} = P \left(1 + \frac{r}{100}\right)^t - P \]
Using the values:
\[ \text{CI} = 20000 \left(1 + \frac{5}{100}\right)^2 - 20000 \]
\[ \text{CI} = 20000 \left(1.05\right)^2 - 20000 \]
\[ \text{CI} = 20000 \left(1.1025\right) - 20000 \]
\[ \text{CI} = 22050 - 20000 = 2050 \]

Thus, the compound interest earned in 2 years is Tk. 2050, making option A the correct answer.