Question

At what rate percent per annum will Rs $6000$ amount to Rs $6615$ in $2$ year when interest is compounded annually?

Answer 1

Hint: The addition of interest to the principal sum of deposit So, that the interest in the next period is then earned on the principal sum plus previously accumulated interest is Compound interest. To solve this we have to use the formula of compound interest.

Complete step-by-step solution:
We have A= $6615$ , P= $6000$ and T= $2yr$
Putting the values in the formula
 $A = P{\left(1 + \dfrac{R}{{100}}\right)^T}$
 $6615 = 6000{\left(1 + \dfrac{R}{{100}}\right)^2}$
 $6000$ will shift towards left side in division
 $\dfrac{{6615}}{{6000}} = {\left(1 + \dfrac{R}{{100}}\right)^2}$
When we divide $\dfrac{{6615}}{{6000}}$ we get $1.025$
$1.025 = {\left(1 + \dfrac{R}{{100}}\right)^2}$
Taking square root both the side
$1.05 = \left(1 + \dfrac{R}{{100}}\right)$
1 will shift towards left in subtraction
$1.05 - 1 = \dfrac{R}{{100}}$
 $0.05 = \dfrac{R}{{100}}$
$100$ will shift towards left in multiplication
$5\% = R$
Hence the rate of compound interest will be $5\%$.

Note: Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days between payments.