Question

Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives 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 equal, then the initial investment, in rupees, made by Sunil is

Accepted Answer

B. Scheme interest rate per half-year = $4\%/2 = 2\% = 0.02$. Anil's investment of Rs 22000 for 6 years (12 half-years) yields: $$A_{	ext{Anil}} = 22000 (1.02)^{12}$$ Sunil invests $P$ in the scheme for 5 years (10 half-years), obtaining $P(1.02)^{10}$. Then reinvests it for 1 year at 10% simple interest: $$A_{	ext{Sunil}} = P(1.02)^{10} 	imes 1.10$$ Equating both final amounts: $$P(1.02)^{10} 	imes 1.10 = 22000 (1.02)^{12}$$ $$P 	imes 1.10 = 22000 	imes (1.02)^2$$ $$P 	imes 1.10 = 22000 	imes 1.0404$$ $$P = 20000 	imes 1.0404 = 20808$$.

Compound Interest and Simple Interest Reinvestment

Explanation

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