Question

The difference between the compound interest and the simple interest on a certain sum for 2 years at 5% per annum is $40 .Find the sum?

Answer 1

Here, given that difference b/w Compound interest & simple interest on a certain sum for 2 years at 5% per annum is $40.

We have to find out sum of money

Solution:-

Formulas used :

• Simple interest = (P × r × n)/100
• Compound interest = P(1 + r)ⁿ - P

According to question:

→ [P(1 + r)ⁿ - P] - (P × r × n)/100 = 40

→ [P(1 + 5%)² - P] - (P × 5 × 2)/100 = 40

→ [P(1 + 0.05)² - P] - (10P/100) = 40

→ [P(1.05)² - P] - (P/10) = 40

→ [P × 1.1025 - P] - (P/10) = 40

→ [1.1025P - P] - (P/10) = 40

→ 0.1025P - P/10 = 40

→ 1025P/10000 - P/10 = 40

→ (1025P - 1000P)/10000 = 40

→ 25P = 40 × 10000

→ 25P = 400000

→ P = 400000/25

→ P = $16,000

Therefore,

∴ Sum of money = $16,000 .

Answer 2

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$\huge \tt {Question:}$

The difference between the compound interest and the simple interest on a certain sum for 2 years at 5% per annum is $40 .Find the sum.

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$\huge \tt {Formula~Used:}$

SI = (P×R×N)/100

CI = P(1+R)^n - P

P = Sl-CI

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$\huge \tt {Solution:}$

Sum/Principal = Difference between SI & Cl = SI-CI

=>[P(1+r)^n -P] - (P × R × N)/100 = $40

=>[P(1 + 0.05)² -P] - (10P/100) = $40

=>[P(1.05)² -P ] - (P/10) = $40

=>[P × 1.102 -P]- (P /10) =$40

=>1025P/10000-P/10 = $40

=>25P = 400000

=>P = 400000/25

=>P = $16000

Sum of money=$16,000

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