Question

find the compound interest as given in question​

Answer 1

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

★ Rs. 2,400 is compounded annually at the rate 5% per annum for 2 ½ years

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

★ The compound interest corrected to the nearest rupee

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

➼ The compound interest on the following sum of money is Rs.312.15 ≈ Rs.312

${ \underline{ \large{ \pmb{ \sf{Understanding \: Concept...}}}}}$

☀️ Concept : As we have been given the principal amount, the rate of interest and the time period. So, we have to find the compound interest on the sum of money. Here, As we have been given the time in the from of mixed fraction which is 2 ½ years, Firstly let's find the compound interest for 2 years and then for the rest half year.

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

~ Now let's find the compound interest for the first 2 years

Using the below mentioned formula to find the amount and later subtract the principal from it to find the compound interest

➼ Formula:

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

~ Where:

• A denotes Amount
• P denotes Principal
• r denotes Rate
• n denotes Time [ No. of Years]

✪ Now, let's substitute the values in the above formula and find the Amount for the first two years.

${ : \implies} \sf \: Amount \: = Principal \bigg[1 + \frac{rate}{10} \bigg] {}^{time}$

${ : \implies} \sf Amount = 2400 \bigg[1 + \frac{5}{100} \bigg ] {}^{2}$

${ : \implies} \sf Amount = 2400 \bigg[ \frac{100}{100} + \frac{5}{100} \bigg] {}^{2}$

${ : \implies} \sf Amount = 2400 \bigg[ \frac{105}{100} \bigg ] {}^{2}$

${ : \implies} \sf Amount = 2400 \times \dfrac{105}{100} \times \dfrac{105}{100}$

${ : \implies} \sf Amount = \cancel\dfrac{26460000}{10000}$

${ : \implies} \sf { \boxed{ \pmb{ \frak{Amount =2646}}} \bigstar}$

• Henceforth the Amount is Rs. 2646

~ Now let's Find the Compound Interest using the below mentioned formula

$\: \: \: \: \: \: \: \dag \: \bigg[ \bf \: Compound \: Intrest = A - P \bigg]$

~ Here,

• Amount = Rs. 2646
• Principal = 2400

~ Substituting the following values in the above mentioned formula let's find the compound Interest

➼ C.I = A - P

➼ C.I = 2646 - 2400

➼ C.I = Rs.246

• Henceforth the Compound Interest for 2 years is Rs. 246

~ Now let's find the Compound Interest for the rest half year Using the formula to find simple interest which is mentioned below.

$\: \: \: \: \: \: \: \dag \: \bigg[ \bf \: S.I = \dfrac{p \times t \times r}{100} \bigg]$

~ Where,

• S.I = Simple interest
• P = Principal
• T = Time
• R = Rate of Interest

~ Here,

• Principal = 2646
• Time = ½ Year
• Rate = 5%

~ Now let's substitute the values and find the compound interest for the next half year

${ : \implies} \sf S.I = \dfrac{P \times T \times R}{100}$

${ : \implies} \sf S.I = \dfrac{2646 \times \dfrac{1}{2} \times 5 }{100}$

${ : \implies} \sf S.I = \dfrac{2646 \times 5}{100 \times 2}$

${ : \implies} \sf{ \boxed{ \pmb{ \frak{S.I = 66.15}}}}$

• Henceforth the compound interest for the next ½ year is 66.15

~ Now let's Add up both of them to find the total compound interest

➼ C.I = 246 + 66.15

➼ C.I = 312.15 ≈ Rs. 312

• Henceforth the Compound Interest is Rs.312.15 when rounded to nearest rupee

${ \underline{ \large{ \pmb{ \sf{Additional\: Information ...}}}}}$

• Formula to Find amount when compounded half yearly

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

• Formula to find amount when compounded quarterly

${ : \implies} \bf A = P\bigg[ 1 + \frac{r}{400} \bigg ] {}^{3n}$

• Formula to find Amount at different rate of interests

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