Find the amount and the compound interest on ₹50000 for $1\dfrac{1}{2}$ years at 8% per annum, the interest being compounded semi-annually.

Since, the rate of interest is 8% per annum, therefore, the rate of interest half-yearly = $\dfrac{1}{2}$ of 8% = 4%.

Principal for first half-year = ₹50000.

Interest for first half-year = $\dfrac{50000 \times 4 \times 1}{100} = \dfrac{200000}{100}$ = ₹2000.

Amount after first half-year = ₹50000 + ₹2000 = ₹52000.

Principal for second half-year = ₹52000.

Interest for the second half-year = $\dfrac{52000 \times 4 \times 1}{100} = \dfrac{208000}{100}$ = ₹2080.

Amount after one year = ₹52000 + ₹2080 = ₹54080.

Principal for third half-year = ₹54080.

Interest for the third half-year = $\dfrac{54080 \times 4 \times 1}{100} = \dfrac{216320}{100}$ = ₹2163.20

Amount after $1\dfrac{1}{2}$ year = ₹54080 + ₹2163.20 = ₹56243.20

Compound interest for $1\dfrac{1}{2}$ year = Final amount - principal = ₹56243.20 - ₹50000 = ₹6243.20

Hence, the amount and the compound interest on ₹50000 for $1\dfrac{1}{2}$ years at 8% per annum, the interest being compounded semi-annually are ₹56243.20 and ₹6243.20 respectively.