Final answer:
To find the principal and rate of interest, we use the compound interest formula to create equations for two time periods provided. By solving these equations simultaneously, we determine the initial investment and the annual interest rate. These values then allow us to calculate the compound interest for the 4th year alone.
Step-by-step explanation:
The question involves calculating the principal and rate of interest in a scenario where compound interest is applied to an investment. To find the answers, one can use the formula for compound interest, which is Principal(1 + rate)^time. Given that the compound amount after 1 year is Rs 55,000 and after 3 years is Rs 66,550, we can create two equations to solve for the principal and the annual interest rate.
Let's denote the principal as P and the annual interest rate as r. Our equations based on the compound interest formula will then be:
- P(1 + r) = 55,000 (for the 1st year)
- P(1 + r)^3 = 66,550 (for the 3rd year)
We can solve these equations simultaneously to find values of P and r. Once we have these values, we can calculate the compound interest for the 4th year by using the compound interest formula with the principal and the rate determined, and raising it to the power of 4. Then we subtract the amount after 3 years to obtain the interest of the 4th year only.