Question

. Find the amount and compound interest on र 16,000 at 15% per annum for 2 1/3
years.​

Answer 1

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\red{correct\;question \: \;:}}}}}\\ \\\end{gathered}$

Q. Find the amount and the compound interest on ₹16,000 at 15% per annum for 2 1/3

years.

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{steps \: to \: solve: }}}}}\\ \\\end{gathered}$

Given that :

Principal (P) = ₹ 16,000

Rate (R) = 15% per annum

Number of years (N) = 2 1/3 years.

To Find :

• The amount and the compound interest ?

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\purple{Detailed \;explanation\;:}}}}}\\ \\\end{gathered}$

In this question Principal ,Rate and Number of years is given and it is asked that we need to find the required amount and compound interest?

For finding the required amount and compound interest we will put the correct formula and correct value in the formula.

_____________

For Finding the amount first we will put formula :

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\red{a = p(1 + \frac{r}{100 {}^{}}) {}^{n} \;\;}}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\red{a = 16000 \times (1 + \frac{15}{100}) {}^{2} \times (1 + \frac{ \frac{1}{3} \times 15}{100}) {}^{3} \;\;}}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\red{a = 16000 \times \frac{115}{100} \times \frac{115}{100} \times \frac{115}{100} \;}}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\red{∴a =₹ 22,218\;}}}}}\\ \\\end{gathered}$

∴ Amount = ₹ 22,218

___________________

Now for find the Compound Interest :

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\green{\;compound \: interest \: = amount - principal}}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\green{compound \: interest \: =₹ 22,218 - ₹16000\;}}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\green{∴compound \: interest \: = ₹6,218\;}}}}}\\ \\\end{gathered}$

∴ Compound Interest = ₹6,218

__________________

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{∴Required\;Answers \: \;:}}}}}\\ \\\end{gathered}$

Amount = ₹22,218

Compound Interest = ₹6,218.

_____________________________

$\dagger \underline{\large \: \: {\frak{Points \: to \: remember : }}}$

• If a person takes a loan from institues like bank or patapehi with fixed rate of interest . After stipulated time he repays the loan with some more money. The additional money is called interest.
• We have learnt that how to find the simple interest = P×R×N/100
• In this formula I = Interest , P = Principal , N = Number of years and R= Rate of interest at p.c.p.a . This is how simple interest is calculated.
• Sometimes the interest is calculated at ab interval of six months . For the duration of N years , if the rate is R and if the interest to be calculated six monthly then the rate is to be taken as R/2 and the duration is considersd as 2N stages of six months.
• Many banks charges the compound interest monthly . At that time they take the interest rate as R/12 monthly and the duration is taken 12×N stages of months and interest is calculated.
• Now a days banks calculate compound interest daily.

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\red{Important \;Formula \: to \: be \: used \: in \: these \: types \: of \: questions \: \;:}}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\purple{1. \: \: \: a = p(1 + \frac{r}{100 {}^{}}) {}^{n} \;\;}}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\purple{ \: 2. \: \: \;compound \: interest \: = amount - principal}}}}}\\ \\\end{gathered}$

Answer 2

★ Given : ↴

• Principal = Rs. 16000
• Time = 2 $\frac{1}{3}$
• Rate of Interest = 15% per annum

★ Find = ↴

We need to Find Amount and Compound Interest.

★ Amount = ↴

$P(1 + \frac{R}{100})^{n} (1 + \frac{TR}{100} )$

★ Amount = ↴

$16000 \times (1 + \frac{15}{100})^{2} \times(1 + \frac{ \frac{1}{3} \times 15 }{100})$

★ Amount = ↴

$16000 \times \frac{115}{100} \times \frac{115}{100} \times \frac{115}{100}$

Amount (A) ↧

$\boxed {\mathrm { \longrightarrow Rs. 22,218}}$

Now Our Amount is Rs 22,218 and we need to Find the Compound Interest.

Compound Interest ⍗

22,218 - 16,000 ↴

$\boxed {\mathrm { \longrightarrow Rs. 6218}}$