Question

Pawan borrowed Rs. 30,000 from a greedy money lender for a certain rate of compound interest and agreed to return it after 1 year. As he could not pay it at the end of the year, the interest rate was increased by 10%. As Pawan could not pay the debt the second year, the money lender increased the interest rate by another 20%. If Pawan closed the loan by paying an interest of Rs. 33590.625 at the end of the third year, find the initial interest rate.

• A. 15%
• B. 20%
• C. 25%
• D. 30%
• E. 33.33%

Answer 1

The Correct Option is C

Let the initial interest rate be \(r\%\).

Interest rate for the second year = \((1+10\%)r\% = 1.1r\%\)

Interest rate for the third year = \((1+20\%)1.1r\% = 1.32r\%\)

Then, \(30,000 + 33590.625 = 30,000(1+r\%)(1+1.1r\%)(1+1.32r\%)\)

\(\frac{63590.625}{30000} = \bigg(\frac{211.96}{100}\bigg) = (1+r\%)(1+1.1r\%)(1+1.32r\%)\)

Using options:

Option A: \((1+15\%)(1+16.5\%)(1+19.8\%) = \frac{160.5}{100}\)

Option B: \((1+20\%)(1+22\%)(1+26.4\%) = \frac{185.04}{100}\)

Option C: \((1+25\%)(1+27.5\%)(1+33\%) = \frac{211.96}{100}\)

Hence, option C is the correct answer.