Question

find the compound interest on 8000 for 1 year at 10% p.a for yearly payable​

Answer 1

Answer:

• Compound Interest is ₹800.

Given:

• Principal = ₹8000
• Rate = 10%
• Time = 1 year

To Find:

• Compound interest = ??

Process:

To find the compound interest we first need to find the Amount. To find Amount we need Principal, Rate and Time, which are given. Now we can calculate Amount by using the formula:

$\circ \;\;A = P\bigg(1+\dfrac{R}{100}\bigg)^n$

Where,

P = Principal

R = Rate

n = Time

Now, we can subtract Principal from Amount to get the Compound Interest.

Solution:

As we know that,

$A = P\bigg(1+\dfrac{R}{100}\bigg)^n$

After substituting the values, we get:

$A = 8000\bigg(1+\dfrac{10}{100}\bigg)^1$

After cutting the zeros, we get:

$A = 8000\bigg(1+\dfrac{1\!\!\!\not{0}}{10\!\!\!\not{0}}\bigg)^1\\\\A = 8000\bigg(1+\dfrac{1}{10}\bigg)^1$

Solving further, we get:

$A = 8000\bigg(\dfrac{10+1}{10}\bigg)^1\\\\A = 8000\bigg(\dfrac{11}{10}\bigg)^1$

After opening the brackets, we get:

$A = 8000\times\dfrac{11}{10}$

After cutting the zeros, we get:

$A = 800\!\!\!\not{0}\times\dfrac{11}{1\!\!\!\not{0}}\\\\A = 800\times\dfrac{11}{1}\\\\A = 800\times11\\\\A = 8800$

Hence, Amount = ₹8800

Now,

Compound Interest = (Amount - Principal)

= ₹(8800 - 8000)

= ₹800

Hence, Compound Interest is ₹800.

Answer 2

Solution :-

Given,

Principal, P = Rs. 8000

Rate of Interest, R = 10% per annum

Time, n = 1 Year

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

By Using the Formula $\mathtt {Amount = P\ \Big (1 + \dfrac{R}{100}\Big)^n}$, we have :

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

$\begin {aligned} \textbf{Amount after 1 Year} &= Rs.\ \Big [8000 \times \Big (1 + \dfrac{10}{100}\Big )^1\Big ]\\\\&= Rs.\ \Big [8000 \times \Big (1 + \dfrac{1}{10}\Big )^1\Big ]\\\\&= Rs.\ \Big [8000 \times \Big (\dfrac{11}{10}\Big )^1\Big ]\\ &\boxed{\because 1 + \dfrac{1}{10} \Rightarrow \dfrac{10 + 1}{10} = \dfrac{11}{10}}\\\\&= Rs.\ 800 \times 11\\ &\boxed{\because 800 \not 0 \times \dfrac{11}{1 \not 0} = 800 \times \dfrac{11}{1} = 800 \times 11}\\\\&= \bf Rs. \ 8800 \end {aligned}$

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

Thus, Amount after a Year = Rs. 8800

And, Compound Interest = (Amount - Principal)

= Rs. (8800 - 8000)

= Rs. 800