Question

) Find the difference between simple interst and compound
interest on Rs. 6250 in 2 years at 4p.c.p.a.​

Answer 1

Given:

• Principal = Rs. 6250
• Time = 2 years
• Rate of interest = 4%

To Find:

• the difference between simple interst and compound interest

Solution:

★ Now,

• Let's first find the simple interest on the following sum of money

★ We know,

$\: \: \: \: \: \: \: \dag \: \bigg [ \bf\: Simple \: Intrest = \dfrac{p \times t \times r}{100} \bigg]$

★ Where,

• P = Principal
• T = Time
• R = Rate of interest

★ Here,

• Principal = Rs.6250
• Time = 2 years
• Rate of interest = 4%

★ Substituting we get,

${ : \implies} \tt SI = \frac{6250 \times 2 \times 4}{100} \\ \\ \\ { : \implies} \tt SI = \frac{6250 \times 4}{50} \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \tt SI = 125 \times 4 \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies}{ \underline{ \boxed{ \pmb{ \frak{ SI = Rs.500}}} \star}} \: \: \: \: \: \:$

• Henceforth, the simple interest is Rs.500

★Now,

• Let's find compound interest

★ We know,

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

★ Where,

• A stands for Amount
• P stands for Principal
• R stands for Rate of interest
• N stands for Time

★ Here,

• Principal = 6250
• Rate = 4%
• Time =2 years

★ Substituting we get,

${ : \implies} \bf \: A = P \bigg [1 + \frac{r}{100} \bigg] {}^{n} \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf \: A = 6250 \bigg [1 + \frac{4}{100} \bigg] {}^{2} \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf \: A = 6250 \bigg [ \frac{100}{100} + \frac{4}{100} \bigg] {}^{2} \\ \\ \\ { : \implies} \bf \: A = 6250 \bigg [\frac{104}{100} \bigg] {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf \: A =6250 \times \frac{104}{100} \times \frac{104}{100} \\ \\ \\ { : \implies} \bf \: A =6250 \times \frac{26}{25} \times \frac{26}{25} \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf \: A = \: 10 \times 26 \times 26 \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf \: A =10 \times 676 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf { \underline{ \boxed{ \pmb{ \frak{ A =Rs.6760}}} \star}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth, the amount is Rs.6760

★ Now,

• Let's find the compound interest

★ We know,

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

★ Where,

• A stands for Amount
• P stands for Principal

★ Here,

• Amount = Rs.6760
• Principal = 6250

★ Substituting we get,

➱ CI = A - P

➱ CI = 6760 - 6250

➱ CI = Rs. 510

• Henceforth the compound interest is Rs. 510

★ Now,

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

★ We know,

• Difference = C.I - S.I

★ Substituting we get,

➱Difference = C.I - S.I

➱ Difference = 510 - 500

➱ Difference = Rs.10

Hence:

• The difference between simple interest and compound interest is Rs. 10

Answer 2

Given :

• Principal (P) = Rs 6250
• Rate (R) = 4% p.a
• Time (T , n ) = 2 years

To Find :

• the difference between simple interest and compound interest

Formulas :

• A = P [1 + R / 100]^n
• CI = A - P
• SI = P × R × T / 100

where ,

• P denotes Principal
• R denotes Rate
• n denotes Time
• T denotes Time
• A denotes Amount
• CI denotes Compound Interest
• SI denotes Simple Interest

Solution :

✰ In this question, we have to find difference between simple interest and compound interest . So Firstly we will find the simple interest and compound interest separately then we will substract them to find the difference.

⠀⠀⠀

⟹ Simple Interest = P × R × T / 100

⟹ Simple Interest = 6250 × 4 × 2 / 100

⟹ Simple Interest = 625 × 4 × 2/10

⟹ Simple Interest = 625 × 8/10

⟹ Simple Interest = 5000/10

⟹ Simple Interest = Rs 500

⠀

Now,

⟼ Amount = P [1 + R / 100]^n

⟼ Amount = 6250 [1 + 4 / 100]²

⟼ Amount = 6250 [104 / 100]²

⟼ Amount = 6250 × 104/100 × 104/100

⟼ Amount = 625 × 104/10 × 104/100

⟼ Amount = 625 × 10,816/1000

⟼ Amount = 6760000/1000

⟼ Amount = Rs 6760

And,

⟼ CI = Amount - Principal

⟼ CI = 6760 - 6250

⟼ Compound Interest = Rs 510

⠀⠀⠀

Finding the difference :

➟ Compound Interest - Simple Interest

➟ 510 - 500

➟ Rs 10

Thus Difference between Compound Interest and Simple Interest is Rs 10

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