Question

Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is

Answer 1

Anil invested $22000$ for $6$ years at $4\%$ interest compounded half-yearly.

Amount = $22000(1+\frac {2}{100})^{12}$

$= 22000 (1.02)^{12}$
Suppose, Sunil invest $P$ rupees for $5$ years at $4\%$ C.I. half-yearly and $10\%$ S.I. for $1$ additional year.

Amount = $P(1+\frac {2}{100})^{10} \times 1.1$

$= P (1.02)^{10} \times 1.1$
Given, both amounts are same,

$22000 (1.02)^{12}= P (1.02)^{10} \times 1.1$
$P = \frac {22000 (1.02)^{12}}{(1.02)^{10} \times 1.1}$

$⇒P = \frac {22000 (1.02)^{2}}{1.1}$
$⇒P=20808$

So, the correct option is (C): $20808$