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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

Explanation:

Half yearly interest = 4/2 = 2%.

Amount Anil gets after 6 years = 22000 × ${(1 + \frac{2}{100})}^{6 \times 2}$

Let the amount which Sunil invests = S.
Amount Sunil gets after 5 years = S × ${(1 + \frac{2}{100})}^{5 \times 2}$

Sunil invests this amount for 6^th year at 10% p.a.
∴ Amount Sunil gets at the end of 6 years = S × ${(1 + \frac{2}{100})}^{5 \times 2}$ × 1.1

⇒ S × ${(1 + \frac{2}{100})}^{5 \times 2}$ × 1.1 = 22000 × ${(1 + \frac{2}{100})}^{6 \times 2}$

⇒ S × 1.1 = 22000 × ${(1 + \frac{2}{100})}^{2}$

⇒ S = 20000 × (1.02)²

⇒ S = 20000 × 1.0404 = 20,808.

Hence, 20808.

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