Question

At what rate percent per annum will a sum of 3200 amounts to rs 3872 in two years

Answer 1

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Answer 2

Answer:

          Rate percent per annum = 10%

Explanation:

• Compound interest is the interest imposed on a loan or deposit amount and It is the most commonly used concept in our daily life. The compound interest for an amount depends on both Principal amount and interest gained over periods. This is the main difference between compound and simple interest. Simple interest only depends on the Principal amount.

• Given that the Principal amount = 3200

        After two years total amount = 3872

        Time period or number of years = 2 years

• We know that the total amount 'A', after 'N' years based on compound interest calculation;

A = P × $(1+\frac{R}{100} )^{N}$, where P is the Principal amount and N is the number of years.

⇒ 3872 = $3200 *(1+\frac{R}{100} )^{2}$

⇒ $\frac{3872}{3200}$ = $(1+\frac{R}{100} )^{2}$

⇒ $(\frac{44}{40} )^{2}$ = $(1+\frac{R}{100} )^{2}$

• By taking square root of LHS and RHS ;

$\frac{R}{100}$ = $\frac{44}{40}$ - 1

$\frac{R}{100}$ = $\frac{4}{40}$

$\frac{R}{5}$ = $\frac{4}{2}$

∴ R = 10%

• Hence, rate percent per annum = 10%

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