Question

The Simple Interest on a sum of money for 2 years at 6% per annum
is Rs 900 . what will be the Compound Interest on that sum at the same rate and the same period ?​

Answer 1

Answer:

1248

Step-by-step explanation:

Let principal = x

Time = 2 years

Rate = 6%

Simple interest = 900 rupees

Formula for simple interest = ( PTR ) ÷ 100

=> 900 = (PTR/100)

=> 900 = (P * 2 * 6)/100

=> 900 * 100 = 12P

=> 90000 = 12P

=> P = 7500.

Thus, Principal = 7500.

We have to solve Amount.

A = Principal * ( 1 + ( r/100 ) ) ^ n

=> 7500 * ( 1 + ( 6 ÷ 100 ) ) ²

=> 7500 * ( 1 + ( 4 ÷ 50 ) ) ²

=> 7500 * (54/50) ²

=> 8748

Amount = Principle + interest

8748 = 7500 + Interest

Interest = 1248

Therefore, Compound interest = 1248

#Hope my answer helped you!

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\mathfrak{Suppose,} \\ \\ \mathtt{</p><p>The \: \: sum \: \: of \: \: money \: \: be \: \: Rs. \: P} \\ \\ \underline{ \mathfrak{ \: Given, \: }} \\ \\ \mathtt{Rate \: \: of \: \: Interest, r = 6\%} \\ \\ \mathtt{No. \: \: of \: \: years, n = 2 \: \: years.} \\ \\ \mathtt{S.I. = Rs. 900 }$

$\underline{ \mathfrak{ \: \: We \: \: know \: \: that, \: }} \\ \\ \: \: \: \: \: \: \: \: \mathtt{S.I. = \frac{P \times r \times n}{100} } \\ \\ \mathtt{\Longrightarrow \: 900 = \frac{ P\times 6 \times 2}{100} } \\ \\ \mathtt{\Longrightarrow \:900 = \frac{12P}{100} } \\ \\ \mathtt{\Longrightarrow \:12P = 90000 } \\ \\ \mathtt{\Longrightarrow \: P= \frac{90000}{12} } \\ \\ \mathtt{\therefore \: \: \: P = 7500} \:$

$\bold{Hence,} \\ \: \: \: \: \: \: \: \bold{The \: \: sum \: \: of \: \: money = Rs. \: 7500}</p><p>$

$\mathfrak{Now,} \\ \\ \underline{ \mathfrak{ \: \: We \: \: know \: \: that, \: \: }} \\ \\ \mathtt{C.I. = A - P } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = P(1 + \frac{r}{100}) {}^{n} - P } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ =P(1 + \frac{r}{100} ) {}^{n} - 1 } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = 7500 \times (1 + \frac{6}{100}) {}^{2} - 1 } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = 7500 \times ( \frac{106}{100} ) {}^{2} - 1} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = 7500 \times ( \frac{11236}{10000} - 1)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = 7500 \times ( \frac{11236 - 10000}{10000} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = 7500 \times \frac{1236}{10000} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = \frac{9,270,000}{10000} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \mathtt{ = 927}$

$\bold{Hence,} \\ \: \: \: \bold{Compound \: \: interest \: \: of \: \: the \: \: sum \: \: = Rs. \: 927}</p><p>$