The difference between the simple interest and the compound interest at the same rate for ₹32,000 for 2 years is ₹80. What is the rate of interest, if, in the case of compound interest, interest is compounded annually?

5% per annum

Simple Interest = \(\frac{Principal ×Rate × Time }{100}\)

SI= \(\frac{32000 × Rate × 2 }{100}\) 

With compound interest  , Amount =  P × ( 1 + \(\frac{R}{100}\) )²

ATQ,

Difference in compound and simple interest =  \(\frac{PR²}{ (100)² }\)

 \(\frac{PR²}{ (100)² }\) = 80

 \(\frac{32000× R²}{ (100)² }\)= 80

 \(\frac{32× R²}{ 10 }\)= 80

R² = 25

R = 5

So , Rate is 5%