Question

Find the principle, if the amount of a certain principle after 2years is Rs . 4,036.80 at the rate of 16 p.c.p.a.​

Answer 1

Correct Question:

Find the principal, if the amount of a certain principal after 2 years is Rs. 4,036.80 at the rate of 16 p.c.p.a.​

Given:

• Amount = Rs. 4036.80
• Time = 2 years
• Rate = 16 p.c.p.a

What To Find:

We have to find the principal.

How To Find:

• We have to use the formula of the amount in compound interest.
• Substitute the values.
• Solve the values.
• Find the principal.

Formula Needed:

$\bf Amount = Principal \bigg( 1 + \dfrac{Rate}{100} \bigg) ^{Time}$

Solution:

Using the formula,

$\sf \implies Amount = Principal \bigg( 1 + \dfrac{Rate}{100} \bigg) ^{Time}$

Substitute the values,

$\sf \implies 4036.80 = Principal \bigg( 1 + \dfrac{16}{100} \bigg) ^{2}$

Solve the brackets,

$\sf \implies 4036.80 = Principal \bigg( \dfrac{116}{100} \bigg) ^{2}$

Remove the brackets,

$\sf \implies 4036.80 = Principal \times \dfrac{116}{100} \times \dfrac{116}{100}$

Multiply the fractions,

$\sf \implies 4036.80 = Principal \times \dfrac{13456}{10000}$

Divide 13456 by 10000,

$\sf \implies 4036.80 = Principal \times 1.3456$

Take 1.3456 to LHS,

$\sf \implies \dfrac{4036.80}{1.3456} = Principal$

Divide 4036.80 by 1.3456,

$\sf \implies 3000 = Principal$

Final Answer:

$\underline {\boxed{\huge{\it \therefore Thus, the \: principal \: here \: is \: Rs. \: 3000.}}}$