Final answer:
To find the rate of interest and principal given the compound interest for 2 and 3 years, we can set up two equations and solve them simultaneously using the compound interest formula, where the future value minus the principal gives us the compound interest for each year.
Step-by-step explanation:
The question asks us to find the rate of interest and the principal amount when the compound interest on a sum of money for 2 years is Rs 210 and for 3 years is Rs 331.
Let's denote the principal as 'P' and the annual interest rate as 'r'. According to the compound interest formula:
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- Future Value after n years = P × (1 + r)^n
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- Compound Interest after n years = Future Value - Principal
After 2 years, the compound interest is Rs 210, so:
P × (1 + r)^2 - P = 210
And after 3 years, the compound interest is Rs 331, so:
P × (1 + r)^3 - P = 331
Now, we set up two equations based on the information provided and solve them simultaneously to find 'P' and 'r'.