Question

Find the period.

Answer 1

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 × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

Or, A = p × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or, Rs 17,763 = Rs 9300 × $(1+\dfrac{\textrm 13}{100})^{\textrm t}$

Or, $\dfrac{17763}{9300}$ = $(1.13)^{t}$

or, 1.91 = $(1.13)^{t}$

Taking Log both side

$Log_{10}$1.91 = $Log_{10}$(  $(1.13)^{t}$ )

or, 0.2810 = t × $Log_{10}$1.13

or, 0.2810 = t × 0.0530

∴ t - $\dfrac{0.2810}{0.0530}$

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