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:
Answer & explanation
Correct answer: option 1
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