Answer:
The Time period of the Amount is 5 years 3 days .
Step-by-step explanation:
Given as :
The principal = p = Rs 9300
The annual rate of interest = r = 13%
The Total amount after t years = A = Rs 17,763
Let The time period = t years
From Compound Interest method
Amount = principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, Rs 17,763 = Rs 9300 × [tex](1+\dfrac{\textrm 13}{100})^{\textrm t}[/tex]
Or, [tex]\dfrac{17763}{9300}[/tex] = [tex](1.13)^{t}[/tex]
or, 1.91 = [tex](1.13)^{t}[/tex]
Taking Log both side
[tex]Log_{10}[/tex]1.91 = [tex]Log_{10}[/tex]( [tex](1.13)^{t}[/tex] )
or, 0.2810 = t × [tex]Log_{10}[/tex]1.13
or, 0.2810 = t × 0.0530
∴ t - [tex]\dfrac{0.2810}{0.0530}[/tex]
I.e t = 5.30 years
So, The time period = t = 5 years 3 days
Hence The Time period of the Amount is 5 years 3 days . Answer
