Question

find the compound interest compounded annually on ₹2700, rate 6 2/3 per annum and time is 2 years.
Please answer with explanation and step by step. ​

Answer 1

Solution :-

Given,

Principal, P = Rs. 2700 ;

Rate of Interest, r = $\dfrac{20}{3}\%$ p.a and

Time, n = 2 Years

$\begin {gathered} \end {gathered}$

Using the Formula, $\mathtt {A = Rs.\ P \Big (1 + \dfrac{R}{100} \Big)^n}$, we get -

$\begin {aligned} \textbf {Amount after two Years} & = Rs. \Big [2700 \times \Big (1 + \dfrac{20}{3 \times 100}\Big )^2 \Big ]\\\\\\&\Rightarrow Rs. \Big [2700 \times \Big (\dfrac{16}{15} \Big )^2 \Big ]\\\\\\&\Rightarrow Rs. \Big [2700 \times \dfrac{16}{15} \times \dfrac{16}{15} \Big ]\\\\\\&= \bf Rs.\ 3,072 \end {aligned}$

Thus,

Amount after 2 Years = Rs. 3,072

∴ Compound Interest = Rs. (3,072 - 2700) = Rs. 372

$\begin {gathered} \end {gathered}$

Additional Information :-

Applications for Compound Interest Formula :-

In each of the following Situations, the Compound Interest Formula is used :

• Increase or Decrease in Population

• The growth of Bacteria when the Rate of growth is known

• Depreciation in the Values of Machines, etc., at a given Rate

$\begin {gathered} \end {gathered}$

Additional Formulae :-

$\mathtt{Compound\: Interest = (Amount) - (Principal)}$

ii. If Principal = Rs. P, Rate of Interest = R% p.a and Time = n Years, then -

$\begin {gathered} \end {gathered}$

(a) Amount after n Years (Compounded Half - Yearly)

$\mathtt{= Rs.\ P \Big (1 + \dfrac{R}{2 \times 100}\Big)^{2n}}$

(b) Amount after n Years (Compounded Quarterly)

$\mathtt{= Rs.\ P \Big (1 + \dfrac{R}{4 \times 100}\Big)^{4n}}$

Answer 2

Answer:

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