Find the annual rate of interest. Principal = 4600 rupees, Period = 5 years, Total amount = 6440 rupees, Annual rate of interest = __%

Answer:The rate of interest for compounded annually is 6.96 %  . Step-by-step explanation:Given as :The principal amount = Rs 4600The time period = 5 yearsThe amount after 5 years = Rs 6440Let The rate of interest = R %From compounded methodAmount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm Time}[/tex]or, Rs 6440 = Rs 4600 × [tex](1+\dfrac{\textrm R}{100})^{\textrm 5}[/tex]Or, [tex]\frac{6440}{4600}[/tex] =  [tex](1+\dfrac{\textrm R}{100})^{\textrm 5}[/tex]or, 1.4 =  [tex](1+\dfrac{\textrm R}{100})^{\textrm 5}[/tex]Or, [tex](1.4)^{\frac{1}{5}}[/tex] = 1 + [tex]\dfrac{R}{100}[/tex]or, 1.0696 =  1 + [tex]\dfrac{R}{100}[/tex]or, [tex]\dfrac{R}{100}[/tex] = 1.0696 - 1Or, [tex]\dfrac{R}{100}[/tex] = 0.0696∴ R = 0.0696 × 100I.e R = 6.96Hence The rate of interest for compounded annually is 6.96 %  .  Answer