Question

p= 5000, r=9%, t= 1.5 year. find the compound interest​

Answer 1

${\large{\underline{\pmb{\sf{Given...}}}}}$

★ the amount Rs. 5000 is compounded for 1.5 years  at the rate of interest 9%  per annum.

${\large{\underline{\pmb{\sf{To \; Find...}}}}}$

★ The compound interest

${\large{\underline{\pmb{\sf{Understanding\; the \; concept..}}}}}$

☀️ concept : Now, we have been provided with the principal amount which is Rs. 5000, the rate of interest which is 9% and the time which is 1.5 years. so, now let's use the formula to find thee simple interest

❍ Further adding the simple interest to the principal amount and find the simple interest for the next half year which makes it compounded

${\large{\underline{\pmb{\sf{Using\;concept...}}}}}$

✪ Formula to find the simple interest is :

$\tt \dfrac{Principal\times Rate \times Time}{100}$

${\large{\underline{\pmb{\sf{Solution...}}}}}$

★ Th compound interest on the following sum of money is Rs. 245.25

${\large{\underline{\pmb{\sf{Full\; solution...}}}}}$

~ Using the above mentioned formula let's substitute the values and find the simple interest for the first year as we know that simple and the compound interest for the first year is the same.

➝ Here,

• Principal = 5000
• Rate = 9%
• time = 1 year

~ now let's substitute these values in the formula

➟ S.I = P × t  × R / 100

➟ S.I = 5000 × 1 ×9 / 100

➟ SI. = 50 × 1 × 9

➟ S.I = 450

• Henceforth the interest for the first year is Rs.450

~ Now, let's add up the interest which we found to the principal amount and  find the interest for the next half year which is left.

• Principal = 5000 + 450
• Principal = 5450

~ now let's substitute the values in the formula mentioned above and find the interest,

➟ S.I = P × T × R / 100

➟ S.I = 5450 × 0.5   9 / 100

➟ S.I = 2750 × 9 / 100

➟ S.I = 24525 / 100

➟ S.I = 245.25

• henceforth the compound interest is rs 245.25

${\large{\underline{\pmb{\sf{ Additional \; Info...}}}}}$

• Direct formula to find amount when it's compounded annually

$\bf :\implies A = P \bigg[ 1 + \frac{r}{100} \bigg]^{n}$

• Formula to find amount when compounded half - yearly

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

• Formula to find amount when compounded quarterly

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

• Formula to find amount at different rate of interests

$\bf :\implies A = P \bigg[ 1 + \frac{r_{1} }{100} \bigg] \bigg[ 1 + \frac{r_{2}}{100} \bigg]\bigg[ 1 + \frac{r_{3}}{100} \bigg]$

*Note : You can subtract the principal form the amount to find the compound interest in further

Answer 2

Step-by-step explanation:

${\large{\underline{\pmb{\sf{Given...}}}}}Given...Given...</p><p></p><p>★ the amount Rs. 5000 is compounded for 1.5 years  at the rate of interest 9%  per annum.</p><p></p><p>{\large{\underline{\pmb{\sf{To \; Find...}}}}}ToFind...ToFind...</p><p></p><p>★ The compound interest</p><p></p><p>{\large{\underline{\pmb{\sf{Understanding\; the \; concept..}}}}}Understandingtheconcept..Understandingtheconcept..</p><p></p><p>☀️ concept : Now, we have been provided with the principal amount which is Rs. 5000, the rate of interest which is 9% and the time which is 1.5 years. so, now let's use the formula to find thee simple interest</p><p></p><p>❍ Further adding the simple interest to the principal amount and find the simple interest for the next half year which makes it compounded</p><p></p><p>{\large{\underline{\pmb{\sf{Using\;concept...}}}}}Usingconcept...Usingconcept...</p><p></p><p>✪ Formula to find the simple interest is :</p><p></p><p>\tt \dfrac{Principal\times Rate \times Time}{100}100Principal×Rate×Time</p><p></p><p>{\large{\underline{\pmb{\sf{Solution...}}}}}Solution...Solution...</p><p></p><p>★ Th compound interest on the following sum of money is Rs. 245.25</p><p></p><p>{\large{\underline{\pmb{\sf{Full\; solution...}}}}}Fullsolution...Fullsolution...</p><p></p><p>~ Using the above mentioned formula let's substitute the values and find the simple interest for the first year as we know that simple and the compound interest for the first year is the same.</p><p></p><p>➝ Here,</p><p></p><p>Principal = 5000</p><p></p><p>Rate = 9%</p><p></p><p>time = 1 year</p><p></p><p>~ now let's substitute these values in the formula</p><p></p><p>➟ S.I = P × t  × R / 100</p><p></p><p>➟ S.I = 5000 × 1 ×9 / 100</p><p></p><p>➟ SI. = 50 × 1 × 9</p><p></p><p>➟ S.I = 450</p><p></p><p>Henceforth the interest for the first year is Rs.450</p><p></p><p>~ Now, let's add up the interest which we found to the principal amount and  find the interest for the next half year which is left.</p><p></p><p>Principal = 5000 + 450</p><p></p><p>Principal = 5450</p><p></p><p>~ now let's substitute the values in the formula mentioned above and find the interest,</p><p></p><p>➟ S.I = P × T × R / 100</p><p></p><p>➟ S.I = 5450 × 0.5   9 / 100</p><p></p><p>➟ S.I = 2750 × 9 / 100</p><p></p><p>➟ S.I = 24525 / 100</p><p></p><p>➟ S.I = 245.25</p><p></p><p>henceforth the compound interest is rs 245.25</p><p></p><p>{\large{\underline{\pmb{\sf{ Additional \; Info...}}}}}AdditionalInfo...AdditionalInfo...</p><p></p><p>Direct formula to find amount when it's compounded annually</p><p></p><p>\bf :\implies A = P \bigg[ 1 + \frac{r}{100} \bigg]^{n}:⟹A=P[1+100r]n</p><p></p><p>Formula to find amount when compounded half - yearly</p><p></p><p>\bf :\implies A = P \bigg[ 1 + \frac{r}{200} \bigg]^{2n}:⟹A=P[1+200r]2n</p><p></p><p>Formula to find amount when compounded quarterly</p><p></p><p>\bf :\implies A = P \bigg[ 1 + \frac{r}{400} \bigg]^{4n}:⟹A=P[1+400r]4n</p><p></p><p>Formula to find amount at different rate of interests</p><p></p><p>\bf :\implies A = P \bigg[ 1 + \frac{r_{1} }{100} \bigg] \bigg[ 1 + \frac{r_{2}}{100} \bigg]\bigg[ 1 + \frac{r_{3}}{100} \bigg]:⟹A=P[1+100r1][1+100r2][1+100r3]</p><p></p><p>*Note : You can subtract the principal form the amount to find the compound interest in further</p><p></p><p>$