Answer:
The rate of interest for compounded annually is 6.96 % .
Step-by-step explanation:
Given as :
The principal amount = Rs 4600
The time period = 5 years
The amount after 5 years = Rs 6440
Let The rate of interest = R %
From compounded method
Amount = 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 - 1
Or, [tex]\dfrac{R}{100}[/tex] = 0.0696
∴ R = 0.0696 × 100
I.e R = 6.96
Hence The rate of interest for compounded annually is 6.96 % . Answer
