The difference in compound interest on a certain sum at 10% p.a. for one year, when the interest is compounded half yearly and yearly, is ₹88.80. What is the simple interest on the same sum for $1\frac{2}{3}$ years at the same rate?
Answer & explanation
Correct answer: option 4
Rate of compound interest for 1 year ( compounded annually ) = 10%
Rate of compound interest for 6 months ( compounded half yearly ) = 5%
Net interest rate when interest in compounded half yearly = 5 + 5 + \(\frac{ 5 × 5 }{100}\)
= 10.25%
ATQ,
Required difference = 10.25% - 10% = 0.25%
0.25% = 88.80
1% = 355.2
Sum = 100% = 100 × 355.2 = Rs. 35520
Now,
Simple Interest = \(\frac{P×R×T }{100}\)
= \(\frac{35520 × 10 × 5 }{3 ×100}\)
= \(\frac{35520 }{3 × 2}\)
= Rs. 5920