Question

At what rate per cent per annum will rs640 amount to rs 774.40 in 2 years when compounded annually

Answer 1

Hi !!!!!!!

Here is your answer,

Principal (P) = Rs. 640
Rate of interest (R) = R%
Time (n) = 2 years
Amount = Rs. 774.40


$Amount = P {(1 + \frac{R}{100} )}^{n} \\ \\ = > 774.40 = 640 {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{77440}{100} = 640 {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{7744}{10} = 640 {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{7744}{10} \div 640 = {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{7744}{10} \times \frac{1}{640} = {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{7744}{6400} = {(1 + \frac{R}{100} )}^{2} \\ \\ (7744 = {88}^{2} \: \: and \: \: 6400 = {80}^{2} ) \\ \\ = > ({ \frac{88}{80} )}^{2} = {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{88}{80 } = 1 + \frac{R}{100} \\ \\ = > \frac{88}{80} - 1 \: \: = \: \: \frac{R}{100} \\ \\ = > \frac{88 - 80}{80} = \frac{R}{100} \\ \\ = > \frac{8}{80} = \frac{R}{100} \\ \\ = > \frac{8}{80} \times 100 = R \\ \\ = > \frac{800}{80} = R \\ \\ = > 10 = R$

Rate of interest = 10%


Hope it helps !!!!!!!!!!

Answer 2

Given Principle(P) = Rs 640
           Amount (A)= Rs 774.40
           time (n) = 2 years
A = P(1+r/100)^n
⇒ 774.40 = 640(1+r/100)²
⇒ 774.40/600 = ([100+r]/100)²
⇒ 1.21 = ([100+r]/100)²
⇒ √1.21 = (100+r)/100
⇒ 1.1 = (100+r)/100
⇒ 1.1*100 = 100+r
⇒ r = 110 - 100 = 10%
  Rate of interest = 10%