Question

The compound interest on an amount for 2 years at 5% per annum compounded annually is ₹205. The simple interest is:

• A. ₹250
• B. ₹220
• C. ₹200
• D. ₹210

Answer 1

Answer:

C. ₹200

Solution:

GIVEN:

Time(n) = 2 years, Rate(R) = 5% per annum and Interest(I) = Rs 205

FORMULA USED:

$A = P (1 +\frac{R}{100})$

Where A → Amounts → (Principal + Interest),

P → Principal

R → Rate per annum

n → Number of years

Simple Interest (S.I) = $\frac{P\times{R}\times{T}}{100}$

CALCULATION:

$A = P (1 +\frac{R}{100})$

⇒ $(P + 205) = P (1 + \frac{5}{100})^2$

⇒ $(P + 205) = P (1 + \frac{1}{20})^2$

⇒ $(P + 205) = P\times{\frac{21}{20}}\times{\frac{21}{20}}$

⇒ $P + 205 = \frac{441P}{400}$

⇒$205 = - P + \frac{441P}{400}$

⇒$205 = \frac{41P}{400}$

⇒ P = Rs 2000  

Simple Interest (S.I) $= \frac{P\times{R}\times{T}}{100}$

⇒ S.I = $\frac{2000\times{5}\times{2}}{100}$

∴ Simple Interest is Rs 200.