Question

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

Answer 1

Given :

• Principal = ₹ 6,250
• Rate = 4 p.c.p.a
• Time = 2 years

To Find :

The difference between simple interest and compound interest.

Solution :

We first have to find the simple interest and then the compound interest. After getting both the interests we will subtract the simple interest from the compound interest. And we will get our answer.

Explanation :

Simple Interest :

We know that if we are given the principal, rate and time and is asked to find the simple interest then our required formula is,

Simple Interest = (P × R × T)/100

where,

• P = ₹ 6250
• R = 4%
• T = 2 years

Substituting the values,

⇒ SI = (6250 × 4 × 2)/100

⇒ SI = (625 × 4 × 2)/10

⇒ SI = (625 × 4 × 1)/5

⇒ SI = (125 × 4)/1

⇒ SI = 125 × 4

⇒ SI = 500

∴ SI = ₹ 500.

Simple Interest is ₹ 500.

Compound Interest :

We know that if we are given the principal, rate and time and is asked to find the compound interest then our required formula is,

Compound Interest = [P{1 + R/100}ⁿ] - P

where,

• P = ₹ 6250
• R = 4%
• n = 2 years

Substituting the values,

⇒ CI = [6250{1 + 4/100}²] - 6250

⇒ CI = [6250{1 + 1/25}²] - 6250

⇒ CI = [6250{(25 + 1)/25}²] - 6250

⇒ CI = [6250{26/25}²] - 6250

⇒ CI = [6250{26/25 × 26/25}] - 6250

⇒ CI = [6250 × 26/25 × 26/25] - 6250

⇒ CI = [4225000/625] - 6250

⇒ CI = [6760] - 6250

⇒ CI = 6760 - 6250

⇒ CI = 510

∴ CI = ₹ 510.

Compound Interest is ₹ 510.

Now,

Difference = Compound Interest - Simple Interest

where,

• CI = ₹ 510
• SI = ₹ 500

⇒ Difference = ₹ (510 - 500)

⇒ Difference = ₹ 10

∴ Difference = ₹ 10.

The difference between compound interest and simple interest is ₹ 10.

Answer 2

Answer:

$\large{\underline{\frak{\pmb{Given...}}}}$

• ➣ Principle = Rs.6250
• ➣ Time = 2 years
• ➣ Rate = 4 p.c.p.a.

$\large{\underline{\frak{\pmb{To \:Find ...}}}}$

• ➣ Simple Interest
• ➣ Compound Interest
• ➣ Difference between Interests

$\large{\underline{\frak{\pmb{Using \: Formula ...}}}}$

$\odot {\underline{ \boxed{\sf{S.I= \dfrac{P \times R \times T}{100}}}}}$

$\odot{\underline{ \boxed{\sf{C.I={P \bigg( 1 + \dfrac{R}{100} { \bigg)}^{T}- P}}}}}$

$\odot{\underline{ \boxed{\sf{Difference = C.I - S.I}}}}$

Where

• ➠ S.I = Simple Interest
• ➠ C.I = Compound Interest
• ➠ P = Principle
• ➠ R = Rate
• ➠ T = Time

$\large{\underline{\frak{\pmb{Solution...}}}}$

$\bigstar \: \textbf \red{Finding\:The\: Simple\: Interest }$

$: \implies{\sf{S.I= {\bf{ \dfrac{P \times R \times T}{100}}}}}$

• Substituting the values

$: \implies{\sf{S.I= {\bf{ \dfrac{6250 \times4 \times 2 }{100}}}}}$

$: \implies{\sf{S.I= {\bf{ \dfrac{50000}{100}}}}}$

$: \implies{\sf{S.I= {\bf{\cancel\dfrac{50000}{100}}}}}$

$: \implies{\sf{S.I= {\bf{Rs.500}}}}$

$\odot\underline{\boxed{\bf{\purple{S.I={Rs.500}}}}}$

• The Simple Interest is Rs.500

$\bigstar \: \textbf \red{Finding\:The\: Compound\: Interest }$

${ : \implies\sf{C.I={\bf{P \bigg( 1 + \dfrac{R}{100} { \bigg)}^{T}- P}}}}$

• Substituting the values

${ : \implies\sf{C.I={\bf{6250 \bigg( 1 + \dfrac{4}{100} { \bigg)}^{2}- 6250}}}}$

${ : \implies\sf{C.I={\bf{6250 \bigg(\dfrac{100 + 4}{100} { \bigg)}^{2}- 6250}}}}$

${ : \implies\sf{C.I={\bf{6250 \bigg(\dfrac{104}{100} { \bigg)}^{2}- 6250}}}}$

${ : \implies\sf{C.I={ \bf{6250 \bigg( \cancel\dfrac{104}{100} { \bigg)}^{2}- 6250}}}}$

${ : \implies\sf{C.I={\bf{6250 \bigg( \dfrac{26}{25} { \bigg)}^{2}- 6250}}}}$

${ : \implies\sf{C.I={ \bf{6250 \bigg( \dfrac{26}{25} \times \dfrac{26}{25} \bigg){ - 6250}}}}}$

${ : \implies\sf{C.I={ \bf{6250 \bigg( \dfrac{676}{625}\bigg){ - 6250}}}}}$

${ : \implies\sf{C.I={ \bf{ \bigg(6250 \times \dfrac{676}{625}\bigg){ - 6250}}}}}$

${:\implies\sf{C.I={ \bf{ \bigg( \cancel{6250} \times \dfrac{676} {\cancel{625}}\bigg){ - 6250}}}}}$

${ : \implies\sf{C.I={ \bf(10 \times {676) - 6250}}}}$

${ : \implies\sf{C.I={ \bf{6760 - 6250}}}}$

${ : \implies\sf{C.I= \bf{510}}}$

$\odot \underline{\boxed{\bf{\purple{C.I={Rs.510}}}}}$

• The Compound Interest is Rs.510

$\bigstar \: \textbf \red{Finding\:The\: Difference\: between\: Interests }$

$: \implies{\sf{Difference = \bf{C.I - S.I}}}$

• Substituting the values

$: \implies{\sf{Difference = \bf{510-500}}}$

$: \implies{\sf{Difference = \bf{10}}}$

$\odot\underline{\boxed{\bf{\purple{Difference = {10}}}}}$

• Henceforth,The difference between simple interst and compound is Rs.10

$\large{\underline{\frak{\pmb{Know\: More...}}}}$

★ Formula of Principle(P) if Amount and Interest given

$\odot{\boxed{\sf{\purple{P=Amount - Interest}}}}$

★ Formula of Principle (P) if Interest,time and rate given

$\odot{\boxed{\sf{\purple{P = \dfrac{Interest \times 100 }{Time \times Rate}}}}}$

★ Formula of Principle (P) if amount,time and rate given

$\odot{\boxed{\sf{\purple{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}$

★ Formula of Amount if Principle (P) and Interest (I) given

${\odot{\boxed{\sf{\purple{Amount = Principle + Interest }}}}}$