Question

The difference between the compound interest & simple interest on a sum of ₹15000 for 2 years is ₹96 find the rate of interest

Answer 1

||✪✪ GIVEN ✪✪||

• Principal = Rs.15000
• Time = 2 years .
• Difference b/w CI and SI = Rs.96

|| ✰✰ ANSWER ✰✰ ||

Basic Method :-

Lets Assume That, Rate of interest is R% per annum.

Than,

→ SI = (P * R * T)/100

Putting values ,

→ SI = (15000*R*2)/100

→ SI = 300R.

Similarly,

→ CI = Amount - Principal

→ CI = P[ 1 + (R/100)]² - P

→ CI = P[ { 1 + (R/100)}² - 1]

Putting values ,

→ CI = 15000 [ { 1 + (R/100)}² - 1]

→ CI = 15000*[ (100+R/100)² - 1]

→ CI = 15000 *[ {(100+R)² - 100²}/100² ]

→ CI = 15000 * [ { R² + 200R }/100²]

→ CI = 1.5 * [ R² + 200R]

→ CI = 1.5R² + 300R

Difference b/w, CI and SI now,

→ (1.5R² + 300R) - 300R = Rs.96

→ 1.5R² = 96

→ R² = (96/1.5)

→ R² = 64

→ R = 8%

Hence , Required Rate of interest is 8% per annum.

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✫✫ Shortcut Trick ✫✫

Difference Between CI and SI for 2 Years is :-

☛ Difference = [ {Principal * (Rate)²} / (100)² ]

we Have Given Now :-

⇒ Difference = Rs.96

⇒ Principal = Rs.15000

⇒ Let Rate = R% .

Putting values in Our Formula we get :-

☞ 96 = [ {15000*R²} / (100)² ]

☞ 96 * 100 * 100 = 15000 * R²

☞ 960 = 15R²

☞ R² = 64

☞ R = 8% .

Hence , Rate is 8% per annum.

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Answer 2

REFER TO THE ATTACHMENT

The required Rate of interest is 8% per annum.