Question

on what sum of money will the difference between the simple interest and compound interest in 2 yrs at 5% p.a.is 15 rs​

Answer 1

Given :-

• Rate = 5%
• Time = 2 Years.
• Difference b/w CI & SI = Rs.15

Formula used :-

• SI = (P * R * T) / 100
• CI = P[{( 1 + r/100)^T} - 1]

Solution :-

Let us Assume That, The required Principal is Rs.P

Given That,

→ CI - SI = Rs.15

Putting All value Now, in Formula we get,

→ P[{( 1 + 5/100)²} - 1] - [(P * 5 * 2/100)] = 15

→ P[(21/20)² - 1] - (P/10) = 15

→ P[ (441 - 400)/400] - (P/10) = 15

→ (41P/400) - (P/10) = 15

→ (41P - 40P)/400 = 15

→ P = 15 * 400

→ P = Rs.6000 (Ans.)

Hence, Required Principal is Rs.6000 .

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Shortcut :-

Direct Formula :- when Diff. b/w CI & SI for 2 Year is given.

☛ P = [Diff. * 100²] / (Rate)²

Given That,

➪ Diff. = Rs.15

➪ Rate = 5%

Putting Value in Above Formula ,

☞ P = ( 15 * 100 * 100 ) / ( 5 * 5 )

☞ P = 15 * 20 * 20

☞ P = 300 * 20

☞ P = Rs.6000 (Ans.)

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Answer 2

=> Let Principal = P

=> rate = 5% p.a.

=> time = 2yrs.

=> difference between SI and CI = rs.15

=> CI = A - P = P(1 + r/100)^(t) - P = P[(1 + r/100)^(t) - 1]

=> SI = principal * rate * time/100

It is given that, difference between the simple interest and compound interest is rs.15

=> CI - SI = 15

=>P[{( 1 + 5/100)²} - 1] - [(P * 5 * 2/100)] = 15

=> P[(21/20)² - 1] - (P/10) = 15

=> P[ (441 - 400)/400] - (P/10) = 15

=> (41P/400) - (P/10) = 15

=> (41P - 40P)/400 = 15

=> P = 15 × 400

=> P = rs600