Question

the compound interest on 10000 at 12% per annum for 3years compounded annually​

Answer 1

${\large{\underline{\pmb{\frak{Given : }}}}}$

★ A principal of Rs. 10000 at 12% per annum for 3 years compounded annually​.

${\large{\underline{\pmb{\frak{To\;Find : }}}}}$

★ The compound interest on the following principal respectively to the time and rate of interest.

${\large{\underline{\pmb{\frak{Understanding \; the \; concept : }}}}}$

☀️ Concept : Here we have been provided with the principal amount which is Rs. 10000 , the rate of interest which is 12% per annum , the time which is 3 years and said that it is compounded annually.

❍ Now, Let's use the formula to find the amount when compounded annually and further subtract it with the principal to find the compound interest.

${\large{\underline{\pmb{\frak{Using \; concepts : }}}}}$

✪ Formula to find the amount when compounded annually :

 $\tt P \bigg[ 1 + \frac{r}{100} \bigg]^{n}$

✪ Formula to find the compound interest :

 $\tt Amount - principal$

${\large{\underline{\pmb{\frak{Solution : }}}}}$

★ The compound interest on the sum of money is Rs.4049.28

${\large{\underline{\pmb{\frak{Full \; solution : }}}}}$

~ Using the above mentioned formula let's substitute the values of the principal,time and rate to find the amount and further find the compound interest

➝ Here,

• P denotes principal
• R denotes rate of interest
• N denotes no. of years ( time )

~ Now let's substitute the values in these formula

➟ Amount = Principal [ 1 + r/100 ] ^n

➟ Amount = 10,000 [ 1 + 12/100] ^3

➟ Amount = 10,000 [ 100/100 + 12/100] ^3

➟ Amount = 10,000 [ 112/100 ] ^ 3

➟ Amount = 10,000 × 112/100 × 112/100 × 112/100

➟ Amount = 112 × 112 × 112 / 100

➟ Amount = 14,04,928 / 100

➟ Amount = 14,049.28

• Henceforth the amount is Rs. 14,049.28

~Now let's find the compound interest by using the formula mentioned above

➟ Compound Interest = Amount - principal

➟ Compound Interest = 14049.28 - 10000.00

➟ Compound Interest = Rs. 4049.28

• Henceforth the compound interest  is Rs. 4,049.28

${\large{\underline{\pmb{\frak{ Additional \; knowledge : }}}}}$

• the formula to find amount when compounded half yearly

$:\implies \bf Amount = P \bigg[ 1 + \frac{r}{200} \bigg]^{2n}$

• the formula to find amount when compounded quarterly yearly

$:\implies \bf Amount = P \bigg[ 1 + \frac{r}{400} \bigg]^{4n}$

• the formula to find amount when compounded at different rate of interests

${:\implies} \bf Amount = P \bigg[ 1 + \frac{r_1}{100} \bigg]\bigg[ 1 + \frac{r_2}{100} \bigg]\bigg[ 1 + \frac{r_3}{100} \bigg]$

*Note : You can further subtract the principal from the amount to find thee compound interest

Answer 2

Step-by-step explanation:

★ A principal of Rs. 10000 at 12% per annum for 3 years compounded annually.

$Given$

$To \: Find$

★ The compound interest on the following principal respectively to the time and rate of interest.

$Understandingtheconcept$

☀️ Concept : Here we have been provided with the principal amount which is Rs. 10000 , the rate of interest which is 12% per annum , the time which is 3 years and said that it is compounded annually.

❍ Now, Let's use the formula to find the amount when compounded annually and further subtract it with the principal to find the compound interest.

$Usingconcepts$

Formula to find the amount when compounded annually :

$\tt P \bigg[ 1 + \frac{r}{100} \bigg]^{n}P[1+100r]n$

✪ Formula to find the compound interest :

\tt Amount - principalAmount−principal

{\large{\underline{\pmb{\frak{Solution : }}}}}

Solution:

Solution:

★ The compound interest on the sum of money is Rs.4049.28

{\large{\underline{\pmb{\frak{Full \; solution : }}}}}

Fullsolution:

Fullsolution:

~ Using the above mentioned formula let's substitute the values of the principal,time and rate to find the amount and further find the compound interest

➝ Here,

P denotes principal

R denotes rate of interest

N denotes no. of years ( time )

~ Now let's substitute the values in these formula

➟ Amount = Principal [ 1 + r/100 ] ^n

➟ Amount = 10,000 [ 1 + 12/100] ^3

➟ Amount = 10,000 [ 100/100 + 12/100] ^3

➟ Amount = 10,000 [ 112/100 ] ^ 3

➟ Amount = 10,000 × 112/100 × 112/100 × 112/100

➟ Amount = 112 × 112 × 112 / 100

➟ Amount = 14,04,928 / 100

➟ Amount = 14,049.28

Henceforth the amount is Rs. 14,049.28

~Now let's find the compound interest by using the formula mentioned above

➟ Compound Interest = Amount - principal

➟ Compound Interest = 14049.28 - 10000.00

➟ Compound Interest = Rs. 4049.28

Henceforth the compound interest is Rs. 4,049.28

{\large{\underline{\pmb{\frak{ Additional \; knowledge : }}}}}

Additionalknowledge:

Additionalknowledge:

the formula to find amount when compounded half yearly

:\implies \bf Amount = P \bigg[ 1 + \frac{r}{200} \bigg]^{2n}:⟹Amount=P[1+

200

r

]

2n

the formula to find amount when compounded quarterly yearly

:\implies \bf Amount = P \bigg[ 1 + \frac{r}{400} \bigg]^{4n}:⟹Amount=P[1+

400

r

]

4n

the formula to find amount when compounded at different rate of interests

{:\implies} \bf Amount = P \bigg[ 1 + \frac{r_1}{100} \bigg]\bigg[ 1 + \frac{r_2}{100} \bigg]\bigg[ 1 + \frac{r_3}{100} \bigg]:⟹Amount=P[1+

100

r

1

][1+

100

r

2

][1+

100

r

3

]

*Note : You can further subtract the principal from the amount to find thee compound interest