Rakesh took a loan of Rs. $80,000$ from a bank. If the rate of interest is $10\%$ per annum. Find the difference in amounts he would be paying after $\dfrac{3}{2}$ years, if the interest is compounded semi-annually.

Using the formula for compound amount A = P(1 + (r/2)/100)^(2n), the new rate per half-year is 5 per cent and the total number of half-year periods is 3. The calculation is 80000 * (1 + 5/100)^3, which equals 80000 * (21/20)^3. This equals 80000 * (9261/8000), resulting in a final amount of 92610.

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