Question

solve with ans : the compound interest of a sum of money in 1 years and 2 years are Rs 450 and Rs 945 respectively. find the rate of interest compounded yearly and the sum .​

Answer 1

Answer:

• The rate of interest compounded yearly =10%
• The sum compounded is Rs4,500

Step-by-step explanation:

Compound Interest Formula, Amount, $A(n)=P(1+r)^n$

Interest=Amount - Principal

$I=P(1+r)^n-P$

At the end of 1 year, interest =Rs450, therefore:

$450=P(1+r)-P\\450=P+Pr-P\\450=Pr$

At the end of 2 years, interest =Rs945, therefore:

$945=P(1+r)^2-P\\945=P(1+r)(1+r)-P\\945=P(1+r+r+r^2)-P\\945=P(1+2r+r^2)-P\\945=P+2Pr+Pr^2-P\\945=2Pr+Pr^2$

Recall: Pr=450

Therefore:

$945=2(450)+Pr^2\\945-900=Pr^2\\Pr^2=45$

Comparing Pr=450 and $Pr^2=45$

$\dfrac{Pr^2}{Pr}= \dfrac{45}{450}\\r=0.1$

Substitute r=0.1 to obtain P

0.1P=450

P=Rs4500

Therefore:

• The rate of interest compounded yearly =0.1=10%
• The sum compounded is Rs4,500