Question

if the compound interest earned on rupees 30000 at 7% per annum is rupees 4347 , then find the time period ( in years)
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Answer 1

Answer:

2 years.

Step-by-step explanation:

Complete step-by-step answer:

Let the time period be t years.

Now as we know that the compound interest is applied on Rs. 30,000.

So, the principal amount will be = P = Rs. 30,000

Now the amount after t years will be = A = Principal amount + Compound Interest for t years = 30,000 + 4347 = Rs. 34,347.

Now the given compounded rate of interest per annum is = r = 7%.

So, now let us apply compound interest formula.

⇒34,347=30,000(1+7100)t

Dividing both sides of the above equation by 30000.

⇒3434730000=(1+7100)t

⇒1144910000=(107100)t

⇒(107100)2=(107100)t

So, comparing powers of both the sides of the above equation.

t = 2 years

So, the time period will be 2 years

Answer 2

★ Solution :-

$\sf \longmapsto Amount = P \bigg(1 + \dfrac{R}{100} { \bigg)}$

$\sf \longmapsto 34347 = 30000 \bigg(1 + \dfrac{7}{100} { \bigg)}$

$\sf \longmapsto 34347 = 30000 \bigg( \dfrac{100 + 7}{100} { \bigg)}^{n}$

$\sf \longmapsto 34347 = 30000 \bigg( \dfrac{107}{100} { \bigg)}^{n}$

$\sf \longmapsto 34347 = 30000 ( 1.07 {)}^{n}$

$\sf \longmapsto {1.07}^{n} = \dfrac{34347}{30000}$

$\sf \longmapsto {1.07}^{n} = 1.449$

We know that, 1.07² = 1.449. So,

$\sf \longmapsto n = 2$

Therefore, the time period in years is 2 years.