Question

Find the compound interest and the amount for of the following p= 100000 e =15% p.a t =3years

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Answer 1

Answer:

Given :-

• A sum of Rs 100000, rate of interest is 15% per annum and the time period is 3 years.

To Find :-

• What is the amount and compound interest.

Solution :-

☆ First, we have to find the amount :

Given :

• Principal = Rs 100000
• Rate of Interest = 15% per annum
• Time Period = 3 years

According to the question by using the formula we get,

$\implies \sf\boxed{\bold{A =\: P\bigg(1 + \dfrac{r}{100}\bigg)^n}}$

$\implies \sf A =\: 100000\bigg(1 + \dfrac{15}{100}\bigg)^3$

$\implies \sf A =\: 100000\bigg(\dfrac{100 \times 1 + 15}{100}\bigg)^3$

$\implies \sf A =\: 100000\bigg(\dfrac{100 + 15}{100}\bigg)^3$

$\implies \sf A =\: 100000\bigg(\dfrac{115}{100}\bigg)^3$

$\implies \sf A =\: 100000\bigg(\dfrac{115}{100} \times \dfrac{115}{100} \times \dfrac{115}{100}\bigg)$

$\implies \sf A =\: 1{\cancel{00000}} \times \dfrac{1520875}{10\cancel{00000}}$

$\implies \sf A =\: \dfrac{1520875}{10}$

$\implies \sf\bold{A =\: Rs\: 152087.5}$

Hence, the amount is Rs 152087.5 .

☆ Now, we have to find the compound interest :

Given :

• Amount = Rs 152087.5
• Principal = Rs 100000

According to the question by using the formula we get,

$\dashrightarrow \sf\boxed{\bold{Compound\: Interest =\: A - P}}$

$\dashrightarrow \sf Compound\: Interest =\: Rs\: 152087.5 - Rs\: 100000$

$\dashrightarrow \sf\bold{Compound\: Interest =\: Rs\: 52087.5}$

$\therefore$ The amount is Rs 152087.5 and the compound interest is Rs 52087.5 .

Answer 2

Given:-

• Principal amount=100000
• Rate=15%
• Time=3years

To find:-

• Compound Interest

Formula used:-

$\large \blue{\underline{ \green{\boxed{\sf{ \red{p \large{(1 + \frac{r}{100}) ^{n} = SI }}}}}}}$

Where,

• P=Principal amount
• R=Rate
• n=Time(in years)
• SI=Simple interest

Second formula used:-

$\large \blue{\underline{ \green{ \boxed{\sf{ \red {A-P=I}}}}}}$

Where,

• A=Amount
• P=Principal
• I=Interest

Solution:-

We need to find the compounded principal first and then we have to find the compound interest on the given data. To do this we will firstly substitute the numbers in formula and the subtract the result of compound principal with the given principal.

Let's proceed:-

$\large \underline{\sf{ \implies 100000(1 + \frac{15}{100} )^{3} }}$

$\large\underline{\sf{ \implies100000(1 + \frac{100 \times 1 + 15}{100} )^{3} }}$

$\large\underline{\sf{ \implies100000( \frac{115}{100} )^{3} }}$

$\large\underline{\sf{ \implies100000( \frac{115}{100} \times \frac{115}{100} \times \frac{115}{100} ) }}$

$\large\underline{\sf{ \implies \frac{115 \times 115 \times 115}{10} }}$

$\large\underline{ \boxed{\sf{ \red{ \implies152087.5}}}}$

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Calculating the interest we will use second formula:-

$\large\underline{\sf{ \implies I=152087.5 - 100000}}$

$\large \blue{\underline{ \green{ \boxed{{\sf{ \red{ \implies I=52087.5}}}}}}}$

Henceforth, the interest will be of 52087.5 at the given numerical values.

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Basic concept!!

• When the interest is calculated on the amount of the previous year. This is known as interest compounded or Compound interest.
• The short form of compound interest is:(C.I).
• Compound interest is calculated as time in years.
• It can also be calculated as Half-Yearly, Quaterly, Yearly and on the basis of fraction.