Question

Find the difference in compound and simple interest on Rs.17,500 for 3 years
if the rate of interest is 4​

Answer 1

Given:

• Principal(P) = 17500
• Times(n) = 3 years
• Rate of Interest(r) = 4% per annum

To Find:

• The difference between their simple interest and compound interest

Solution:

Now,

• Let's firstly find the compound interest of the investment

${ \underline{ \frak{As \: we \: know \: that}}}$

$\: \: \: \: \: \: \: \: \: \star{ \underline{ \boxed{ { \sf{Amount = Principal(1 + \frac{rate}{100} \big) } {}^{n} }}}}$

And,

$\pink{ \bigstar}{ \underline{ \boxed{ \frak{ compound \: intrest = amount - principal}}}}$

After Substitution we get,

$: \longrightarrow \sf Amount = Principal \bigg(1 + \frac{r}{100} \bigg ) {}^{n} \\ \\ \\ : \longrightarrow \sf Amount = \: 17500 \bigg(1 + \frac{4}{100} \bigg) {}^{3} \: \: \\ \\ \\ : \longrightarrow \sf Amount =17500 \bigg( \frac{100}{100} + \frac{4}{100} \bigg) {}^{3} \\ \\ \\ : \longrightarrow \sf Amount =17500 \bigg( \frac{104}{100} \bigg) {}^{3} \: \: \: \: \: \: \: \: \: \: \\ \\ \\ : \longrightarrow \sf Amount =175 \cancel{00} \times \frac{104}{ \cancel{100}} \times \frac{104}{100} \times \frac{104}{100} \\ \\ \\ : \longrightarrow \sf Amount =175 \times 104 \times \frac{104}{100} \times \frac{104}{100} \\ \\ \\ : \longrightarrow \sf Amount = \frac{175 \times 104 \times 104 \times 104}{10000} \\ \\ \\ : \longrightarrow \sf Amount = \frac{196,851,200}{10000} \\ \\ \\ : \longrightarrow \sf Amount = \orange{rs.19685.12 \bigstar}$

Hence,

• The amount is 19685 rupees

Now, let's find the Compound Interest

$\purple{ \mapsto}\tt \: compound \: intrest = 19685.12 - 17500 \\ \\ \\ \purple{ \mapsto}\tt \: compound \: intrest = \blue{rs.2185.12} \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore,

• The compound interest is rupees 2185.12 rupees

❍Now, Let's find the simple interest:

As we know that,

$\star \: { \underline{ \boxed{ { \mathfrak{simple \: intrest = \frac{p \times t \times r}{100} }}}}}$

After Substitution we get,

$\longrightarrow \tt simple \: intrest = \frac{175 \cancel{00 }\times 3 \times 4}{ \cancel{100}} \\ \\ \\ \longrightarrow \tt simple \: intrest =175 \times 3 \times 4 \: \: \: \: \: \\ \\ \\ \longrightarrow \tt simple \: intrest = \purple{rs.2100 \bigstar} \: \: \: \: \: \: \:$

Hence,

• The simple interest is rupees 2100

Now, Let's find the difference,

$\purple{ \mapsto}\tt \: difference = 2185.12 - 2100 \\ \\ \\ \purple{ \mapsto}\tt \: difference = \blue{85.12rs} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Henceforth,

• The difference between the compound interest and the simple interest is rupees 85.12

Answer 2

Answer:

Hello Arna sis, Kaise ho sis?? :).:)