Question

A sum gives simple interest of 800 for 2 years at the rate of 4% per annum.
Find the compound interest on the same sum at the same rate of interest and
same time period when interest is compounded annually.​

Answer 1

AnswEr :

$\bigstar\:\boxed{\sf Simple \:Interest=\dfrac{Principal \times Rate \times Time}{100}}$

$\rule{150}{1}$

$\underline{\bf{\dag}\:\textbf{Simple Interest Calculation :}}$

$:\implies\tt Simple \:Interest=\dfrac{Principal \times Rate \times Time}{100}\\\\\\:\implies\tt 800=\dfrac{Principal \times 4 \times 2}{100}\\\\\\:\implies\tt \dfrac{800 \times 100}{4 \times 2}=Principal\\\\\\:\implies\tt 100 \times 100 = Principal\\\\\\:\implies\tt Principal = Rs. \:10000$

$\rule{250}{2}$

$\bigstar \:\boxed{\sf{CI = P\bigg[\bigg(1 + \dfrac{r}{100}\bigg)^{t} - 1}\bigg]}$

$\rule{150}{1}$

$\underline{\bf{\dag}\:\textbf{Compound Interest Calculation :}}$

$:\implies\tt CI = P\bigg[\bigg(1 + \dfrac{r}{100}\bigg)^{t} - 1\bigg]\\\\\\:\implies\tt CI = 10000 \times \bigg[\bigg(1 + \dfrac{4}{100}\bigg)^{2} - 1\bigg]\\\\\\:\implies\tt CI = 10000 \times \bigg[\bigg(1 + \dfrac{1}{25}\bigg)^{2} - 1\bigg]\\\\\\:\implies\tt CI = 10000 \times \bigg[\bigg(\dfrac{26}{25}\bigg)^{2} - 1\bigg]\\\\\\:\implies\tt CI = 10000 \times \bigg[\dfrac{676}{625} - 1\bigg]\\\\\\:\implies\tt CI = 10000 \times \dfrac{51}{625}\\\\\\:\implies\tt CI =Rs. (16 \times 51)\\\\\\\implies\boxed{\tt CI =Rs.\:816}$

⠀

$\therefore\:\underline{\textsf{Compound Interest on the sum is \textbf{Rs. 816}}}$

Answer 2

Question :-- A sum gives simple interest of 800 for 2 years at the rate of 4% per annum.Find the compound interest on the same sum at the same rate of interest and

same time period when interest is compounded annually.

Solution (1) :-

Lets Solve it With Basic Method First .

Given :-

• Simple interest = Rs.800
• Time = 2 years .
• Rate = 4 % .
• we know that, Principal = (Simple interest * 100) / (Rate * Time)

Putting all values here, we get,

→ Principal = (800 * 100)/(4*2)

→ Principal = Rs.10000.

Now, we have Find compound interest on this sum , with same rate as 4% per annum and for 2 years.

→ Amount in CI = P(1+R/100)^T

Putting values again, we get,

→ Amount = 10000 * ( 1 + 4/100)²

→ Amount = 10000 * (26/25)²

→ Amount = 10000*26*26/(25*25)

→ Amount = Rs.10816 .

Now, we know,

→ Compound Interest = Amount - Principal

So,

→ CI = 10816 - 10000 = Rs.816 .

Hence, we get, Rs.816 as Compound interest with same sum of money and with same rate and time.

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Now, Lets Solve the Problem with A Nice and Easiest Trick .

Solution (2) :--

First we will see what is the Main Difference b/w a compound interest and Simple interest .

→ Compound interest is Nothing but Interest on Interest. we can find Any Compound interest with Same SI formula also, we just have to Add the interest on previous Interest.

→ Second Thing, we must know that, Simple interest is same in Each year, that means, we get, same amount of interest Every year .

→ In First year Simple interest and Compound interest both are the same..

If we remember These three basic things , we can solve this problem in 15-20 seconds only . Lets see .

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Simple interest of 2 year is given = Rs.800 .

→ So, we can say that, he gets Rs.400 as simple interest Every year. ( As told , simple interest is same Every year. )

→ Now, we can also say that, he gets Rs.400 as Compound interest also in First year. ( As told , Simple interest and compound interest are same in first year. )

So, Now, we have ,

⍟ 1St year. ⍟ 2nd year.

⍟ SI. 400. 400

⍟ CI 400 . 400 + (4 % of 400)

[ CI = interest on Interest ] .

So,

➥ 2nd year CI = 400 + ( 4 % of 400)

➥ CI = 400 + ( 4 * 400/100)

➥ CI = 400 + 16

➥ CI = Rs.416 .

☛ Hence, CI of both Years = 400(First year) + 416(Second year) = 400 + 416 = Rs.816.

⛬ He gets Rs.816 as compound interest For same years , on same amount and same Time.

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“Mathematics is not about numbers, equations, computations, or algorithms. Mathematics is about understanding.”