Simple and Compound Interest — Mains Questions

A person invests ₹X at 10% simple interest for 4 years. Another person invests ₹Y at 10% compound interest, compounded annually, for 2 years. If the total interest earned by both is ₹4200 and X = 2Y, find the values of X and Y.

Compare two investment options: Option A offers 12% simple interest per annum for 5 years. Option B offers 10% compound interest per annum, compounded half-yearly, for 5 years. If a principal of ₹10,000 is invested in each, calculate the difference in the total amount received from both options.

A loan of ₹P is taken at an interest rate of R% per annum. If the difference between the compound interest and simple interest for 3 years is ₹D, derive a formula for D in terms of P and R. Then, using this formula, find the principal if the difference is ₹122 at 10% per annum.