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
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
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
Options
Answer: 20808
Explanation:
Total amount received by Anil at the end of 6 years = 22000 × (1.02)^12 Total amount received by Sunil at the end of 6 years = x × (1.02)^10 × 1.10 Given both amounts are equal: 22000 × (1.02)^12 = x × (1.02)^10 × 1.10 Divide both sides by (1.02)^10 × 1.10: x = 22000 × (1.02)^2 / 1.10 Now calculate: (1.02)^2 = 1.0404 x = 22000 × 1.0404 / 1.10 x = 22888 / 1.10 x = 20808
Explanation:
Total amount received by Anil at the end of 6 years = 22000 × (1.02)^12 Total amount received by Sunil at the end of 6 years = x × (1.02)^10 × 1.10 Given both amounts are equal: 22000 × (1.02)^12 = x × (1.02)^10 × 1.10 Divide both sides by (1.02)^10 × 1.10: x = 22000 × (1.02)^2 / 1.10 Now calculate: (1.02)^2 = 1.0404 x = 22000 × 1.0404 / 1.10 x = 22888 / 1.10 x = 20808
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