Shawn invests one half of his savings in a bond that pays simple interest for 2 years and receives Rs 550 as interest. He invests the remaining half of his savings in a bond that pays compound interest, compounded annually, at the same rate of interest for the same 2 years and receives Rs 605 as interest. What is the value of his total savings before investing in these two bonds?

Introduction / Context:
This question involves two different investments by Shawn, one earning simple interest and the other earning compound interest. Both investments use the same rate and the same time period, and each investment uses half of his total savings. The problem gives the interest earned from each bond and asks for the total initial savings. This requires setting up equations based on both simple and compound interest formulas and solving them together.

Given Data / Assumptions:

• Total savings = S (unknown).
• Each half investment principal = S / 2.
• Time for both investments = 2 years.
• Rate of interest = R% per annum (same for both, unknown).
• Simple interest from first bond in 2 years = Rs 550.
• Compound interest from second bond in 2 years = Rs 605.
• Compounding in the second bond is annual.

Concept / Approach:
For the simple interest bond, the interest is:
SI = (S / 2) * R * 2 / 100 = S * R / 100 This equals 550. For the compound interest bond, the interest after 2 years is:
CI = (S / 2) * [(1 + R / 100)^2 - 1] This equals 605. Using these two equations, we can solve for S and R.

Step-by-Step Solution:
From simple interest: S * R / 100 = 550. So R = 550 * 100 / S. From compound interest: (S / 2) * [(1 + R / 100)^2 - 1] = 605. Substitute R / 100 = 550 / S. Then (1 + R / 100)^2 = (1 + 550 / S)^2. The algebra simplifies, and solving the simultaneous equations gives R = 20% and S = Rs 2750. So Shawn's total savings before investment is Rs 2750.

Verification / Alternative Check:
Check with S = 2750 and R = 20%. First bond: principal = 1375. SI = 1375 * 20 * 2 / 100 = 1375 * 0.4 = Rs 550. Second bond: principal = 1375, CI at 20% for 2 years. Amount factor = (1.20)^2 = 1.44. Amount = 1375 * 1.44 = 1980. CI = 1980 - 1375 = Rs 605, which matches the data. This confirms that S = 2750 is correct.

Why Other Options Are Wrong:
2543, 2534, and 2546 do not satisfy both the simple interest and compound interest conditions simultaneously. Only 2750 produces the exact interest amounts of 550 and 605 for the two bonds.

Common Pitfalls:
Some learners incorrectly assume that the same interest amount should be earned from both bonds. Others may misapply the compound interest formula or forget that each bond uses half the total savings. Algebraic mistakes when solving the simultaneous equations are also common.

Final Answer:
The value of Shawn's total savings before investing in the two bonds is Rs. 2750.