Question

A principal sum of money is lent out at compound interest compounded annually at the rate of 20% per annum for 2 years. It would give Rs 2410 more if the interest is compounded half yearly. Find the principal sum. 

(a) Rs 120000 

(b) Rs 125000 

(c) Rs 100000 

(d) Rs 110000

Answer 1

(c) Rs 100000

Let the principal sum be Rs x. Then, 

Amount (at interest compounded annually)

= x\(\big(1+\frac{20}{100}\big)^2\) = \(\frac{36X}{25}\)

Amount (at interest compounded half yearly)

= x\(\big(1+\frac{10}{100}\big)^4\) = \(\frac{14641X}{10000}\)

Given, \(\frac{14641X}{10000}\)- \(\frac{36X}{25}\) = 2410

\(\Rightarrow\) \(\frac{14641X-14400X}{10000}\) = 2410

\(\Rightarrow\) \(\frac{241X}{10000}\) = 2410 \(\Rightarrow\)x= Rs 100000