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

• A. 20640
• B. 20808
• C. 20860
• D. 20480

Answer 1

Answer: (B)

20808

Answer 2

Anil's Investment: Principal = Rs 22000 Rate of interest = 4 percent per annum compounded half-yearly = 2 percent per half-year Time = 6 years = 12 half-years The formula for the amount is:

Amount = Principal × $(1 + \frac{Rate}{100})^{Time}$

Substituting the given values:

Amount = 22000 × $(1 + \frac{2}{100})^{12}$ ≈ 27816.22

Sunil's Investment: Let the initial investment be P. After 5 years at 4 percent compounded half-yearly, the amount becomes:

This amount is then reinvested for 1 year at 10 percent simple interest. So, the final amount for Sunil = $P \left( 1 + \frac{2}{100} \right)^{10} \left( 1 + \frac{10}{100} \right)$

Given that both amounts are equal: $27816.22 = P \left( 1 + \frac{2}{100} \right)^{10} \left( 1 + \frac{10}{100} \right)$

Solving for P, we get $P \approx 20808$

Therefore, Sunil's initial investment was approximately Rs 20808.