A borrowed a sum of ₹160000 from B at 10% per annum simple interest. At the same time he lent the same sum to C at the same rate on compound interest, compounded semi-annually for 2 years. Find the amount (in ₹) earned by A in the whole transaction.

2481

Simple at the rate of 10% per annum for 2 years = 10% + 10% = 20%

Simple interest = \(\frac{P × R×T }{100}\) 

= \(\frac{160000 × 10 ×2 }{100}\)

= 32000

Rate when interest compounded half yearly = \(\frac{10 }{2}\) = 5%

For 2 years ( compounded half yearly ) , n = 4

Compound interest = Principal × ( 1 + \(\frac{rate }{100}\))4 - Principal

= 160000 × ( 1 + \(\frac{5 }{100}\))4 - 160000

= 160000 × \(\frac{21 }{20}\)× \(\frac{21 }{20}\)× \(\frac{21 }{20}\)× \(\frac{21 }{20}\) - 160000

= 194481 - 160000

= 34481

Difference b/w CI and SI = 34481 - 32000 = Rs. 2481