If we invest Rs. 2,000 at the rate of interest 10% per annum compounded annually for 3 years, then what will be the interest amount ?
Rs. 662
When interest is compounded annually, the interest of each year is added to the principal and the next year's interest is calculated on this larger amount. The amount after n years is \(A = P(1 + \frac{R}{100})^{n}\), and the compound interest is \(\text{CI} = A - P\). Here P = Rs. 2,000, \(R = 10\%\) per annum and \(n = 3\) years.
Working:
\(A = 2000 \times (1 + \frac{10}{100})^{3}\)
\(A = 2000 \times (1.1)^{3}\)
\(A = 2000 \times 1.331\)
A = Rs. 2,662
\(\text{CI} = A - P\)
\(\text{CI} = 2662 - 2000\)
CI = Rs. 662
Check year by year: \(200 + 220 + 242 = 662\)
Rs. 735.262 and Rs. 650.262 do not come from the formula with these values and look like results of wrong decimal handling. Rs. 1,000 is far too large; even simple interest for 3 years would only be \(2000 \times 10 \times \frac{3}{100}\) = Rs. 600, and compound interest is just slightly more than that.
Hence, Rs. 662.
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