Question

What is the difference between
simple interest and compound interest
for 2 years at the rate of 5% on
Roo 10oo​

Answer 1

Appropriate question:

• What is the difference between simple interest and compound interest for 2 years at the rate of 5% on Rs. 1000

Given:

• Principal = Rs. 1000
• Time = 2 years
• Rate of interest = 5%

To Find:

• The difference between the simple interest and compound on the sum of money.

Solution:

★ Now,

• Let's firstly find the simple interest on the money

★ We know that,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \dag \bigg[ \bf \: SI = \dfrac{P \times R \times T}{100} \bigg]$

★ where,

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

★ Here,

• Principal = 1000
• Rate of interest = 5%
• Time = 2 years

★ Substituting we get,

${ : \implies} \tt \: SI = \frac{p \times t \times r}{100} \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \tt \: SI = \frac{10 \cancel{00 }\times 5 \times 2}{ \cancel100} \\ \\ \\ { : \implies} \tt \: SI = 10 \times 5 \times 2 \: \: \: \: \: \\ \\ \\ { : \implies} \tt \: SI ={ \blue{ \underline{ \boxed { \frak{ 100}}} \star}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth, the simple interest is rupees 100

★ Now,

• Let's find the compound interest on the money

★ We know,

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

★ Where,

• A = Amount
• P = Principal
• R = Rate of interest
• N = Time

★ Here,

• Principal = 1000
• Rate = 5%
• Time = 2 years

★ Substituting we get,

${ : \implies} \bf A = P\bigg[ 1 + \frac{r}{100} \bigg]{}^{n} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf A = 1000\bigg[ 1 + \frac{5}{100} \bigg]{}^{2} \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf A = 1000\bigg[ \frac{100}{100} + \frac{5}{100} \bigg]{}^{2} \\ \\ \\ { : \implies} \bf A = 1000\bigg[ \frac{105}{100} \bigg]{}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf A =1000 \times \frac{105}{100} \times \frac{105}{100} \\ \\ \\ { : \implies} \bf A =105 \times \frac{105}{10} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} { \pink{ \underline{ \boxed{ \pmb{ \frak{ A =1102.5}}}} \star}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the amount is 1102.5

★ Now,

• Let's find the compound interest

★ We know,

$\: \: \: \: \: \: \dag \: \bigg \{ \bf compound \: intrest = \: A -P \bigg \}$

★ Where,

• A = Amount
• P = Principal

★ Here,

• Amount = 1,102.5
• Principal = 1000

★ Substituting we get,

• Compound interest = A - P
• Compound interest = 1,102.5 - 1000
• Compound interest = Rs. 102.5

★ Henceforth,

• The compound interest is Rs. 102.5

★ Now,

• Let's find the difference between simple interest and compound interest

★ Difference,

➱ Compound interest - Simple interest

➱ 102.5 - 100

➱ Rs. 2.5

Hence:

• The difference between simple interest and compound interest is rupees 2.5