Compound Interest and Simple Interest Reinvestment

Scheme interest rate per half-year = $4\%/2 = 2\% = 0.02$. Anil's investment of Rs 22000 for 6 years (12 half-years) yields: $A_{\text{Anil}} = 22000 (1.02)^{12}$

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: $A_{\text{Sunil}} = P(1.02)^{10} \times 1.10$

Equating both final amounts: $P(1.02)^{10} \times 1.10 = 22000 (1.02)^{12}$ $P \times 1.10 = 22000 \times (1.02)^2$ $P \times 1.10 = 22000 \times 1.0404$ $P = 20000 \times 1.0404 = 20808$.