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 ₹)
Answer & explanation
Correct answer: option 1
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 )