A sum of money was invested at 10% interest per year, compounded half-yearly for 18 months. If the amount payable on maturity was ₹83,349, what was the sum invested?

₹72,000

Interest is compounded half yearly,

Rate of interest = \(\frac{10}{2}\)% = 5%

From the formula for compound interest, we know,

Amount = P(1+$\frac{R}{100})^t$

83349 = P [ 1 + \(\frac{5}{100}\) ]³

 83349 = P [ \(\frac{21}{20}\) × \(\frac{21}{20}\) × \(\frac{21}{20}\) ]

83349 × \(\frac{20}{21}\) × \(\frac{20}{21}\) × \(\frac{20}{21}\)  = P

P = 72000