A certain sum becomes ₹13650 at 15% p.a. simple interest after 2 years. What will be the amount (in ₹) of the same sum after 1 year at the same rate of interest, if the interest is compounded half yearly? (nearest to a ₹)

12134

Simple at the rate of 15% per annum for 2 years = 15% + 15% = 30%

Let initial sum = 100%

Amount = Initial Sum + Interest

= 100% + 30%

= 130%

ATQ,

130% = 13650

1% = \(\frac{13650}{130}\) = 105

Initial sum = 100% = 100 × 105 = 10500

Rate of interest is compounded half yearly.

So , New rate = \(\frac{15}{2}\)% = 7.5%

So , Amount = Principal × ( 1 + \(\frac{rate}{100}\) )^t

= 10500 × ( 1 + \(\frac{7.5}{100}\) )²

= 10500 × \(\frac{107.5}{100}\)× \(\frac{107.5}{100}\)

= 12134.06

= 12134   ( approx )