There is an 80% increase in an amount in 8 years at simple interest. What will be the amount received for
Rs.6,000 after 2 years at the same rate, when compounded annually?

​Increase in amount in 8 years = 80%

Principal amount = Rs. 6000

Time period = 2 years

​$$\text{Simple Interest (SI)} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}$$​​

​$$A = P \times \left(1 + \frac{r}{100}\right)^t$$​​

​Let the rate of interest be R% per annum.

​$$SI = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}$$​​

​$$0.8 \times \text{Principal} = \frac{\text{Principal} \times R \times 8}{100}$$​​

​$$R = 10\%$$​​

​$$\text{Amount} = \text{Principal} \times \left( 1 + \frac{\text{Rate}}{100} \right)^{\text{Time}}$$​​

​$$\text{Amount} = 6000 \times \left(1 + \frac{10}{100}\right)^2$$​​

​$$\text{Amount} = 6000 \times 1.1^2$$​​

​$$\text{Amount} = \text{Rs.} \ 7260$$

Therefore, the amount received after 2 years at the same rate, when compounded annually, is Rs. 7260.​​