The simple interest on a sum of money for 2 years at certain rate of interest is ₹320. The compound interest, compounded annually on the same sum for the same duration and at the same rate of interest is ₹384. The sum (in ₹) is:

400

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

320 = \(\frac{ P × R × 2}{100}\)

P × R = 16000

Now,

We know ,

Compound interest = P [ ( 1 + \(\frac{ R}{100}\) )² - 1]

384 = P × \(\frac{ R}{100}\) × \(\frac{ (R + 200) }{100}\)

Put P × R = 16000

384 = \(\frac{ 16000}{100}\) × \(\frac{ (R + 200) }{100}\)

384 = 160 × \(\frac{ (R + 200) }{100}\)

384 = 40 × \(\frac{ (R + 200) }{25}\)

9600 = 40R + 8000

40R = 1600

R = 40

Rate = 40%

We know, P × R = 16000

Put R = 40

P × 40 = 16000

P = 400

So, Initial sum = Rs. 400