Question

A certain sum invested at compound interest becomes rs.6,500 after a period of 6 years and rs.7,800 after a further period of 2 more years. The amount due after a further period of 2 more years is

Answer 1

Answer:

Rs.9360

Step-by-step explanation:

WE KNOW THAT amount in compound interest is given by

A= P(1+i)^n

P(1 + i)^6 = 6500

P(1 + i)^8 = 7800

dividing

(1 + i)^2 = 78/65 = 6/5

P (1 + i)^10 = P(1 + i)^8 * (1 + i)^2 = 7800 × 1.2 = 9360

Answer 2

Amount after 10 years $= 9360$

Explanation:  

Given that, Amount after 6 years $= 6500$

Amount after 8 years $= 7800$

As we know that,

Amount = Sum + Interest  $= P + I$

Amount = Sum + Interest   $= P + \frac{P \times R \time T}{100}$

Amount $= P(1 + \frac{R}{100})^{T}$           ( by Binomial theorem)

$A_{1} = 6500 = (1 + \frac{R}{100})^{6}$ ……(1)

$A_{2} = 7800 = (1 + \frac{R}{100})^{8}$ ……(2)

On dividing equation (2) by (1) we get,

$(1 + \frac{R}{100})^{2} = \frac{6}{5}$  

$(1 + \frac{R}{100})^{10} = (1 + \frac{R}{100})^{8}\times(1 + \frac{R}{100})^{2}$

Amount after 10 years $= 7800 \times \frac{6}{5} = 9360$