Question

If a certain sum of money becomes 8000 in 2 years and 27000 in 5 years.Find principal

Answer 1

Answer:

Question is wrongly written ..

( only if ci than its possible , but than we must have R)

Answer 2

If a certain sum of money becomes 8000 in 2 years and 27000 in 5 years, then the principal is Rs. 3555.56.

Step-by-step explanation:

Required formula:

Amount, A = P [1 + $\frac{R}{100}$]ⁿ

Let’s assume for both the cases the principal be denoted as “P” and the rate of interest be denoted as “R”.

For the first case, the sum amounts to 8000 in 2 years, so, based on the formula, we can write the eq. as

8000 = P [1+$\frac{R}{100}$]² …… (i)

For the second case, the same sum amounts to 27000 in 5 years, so, based on the formula, we can write the eq. as

27000 = P [1+$\frac{R}{100}$]⁵ …… (ii)

On dividing eq. (ii) by (i), we get

$\frac{27000}{8000}$ = [P{1+$\frac{R}{100}$}⁵] / [P{1+$\frac{R}{100}$}²]

⇒ $\frac{27}{8}$ = [1+$\frac{R}{100}$]⁵ / [1+$\frac{R}{100}$]²

⇒ $\frac{27}{8}$ = [1+$\frac{R}{100}$]³  

Taking cube roots on both sides

⇒ $\frac{3}{2}$ = 1+$\frac{R}{100}$

⇒ ½ = $\frac{R}{100}$

⇒ R = 50%

Now, Substituting the value of R in eq. (i), we get

8000 = P [1+ $\frac{50}{100}$]²

⇒ 8000 = P [$\frac{3}{2}$]²

⇒ P = $\frac{</strong>8000*2*2<strong>}{</strong>3*3<strong>}$

⇒ P = Rs. 3555.56

Thus, the principal is Rs. 3555.56 .

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