sanju09 wrote:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?
(A) $2750
(B) $5500
(C) $11000
(D) $22000
(E) $44000
We can plug in the answer choices.
When the $550 simple interest is converted to interest compounded annually, Shawn will receive 550/2 = $275 the first year and 605-275 = $330 the second year.
Thus, the correct answer choice must yield $330 as the second year interest.
Answer choice C: 11,000.
Half this amount = 11,000/2 = 5500.
Since 550 is 10% of 5500, the simple interest rate is 10%.
Compounded annually, Shawn will get 5% the first year, 5% the second year.
Amount at end of the first year = 5500 + 275 = 5775.
Interest second year = .05 * 5775 = 288.5.
Eliminate C.
We need a much higher compounded interest rate, so the initial amount must be much lower.
Answer choice A: 2750.
Half this amount = 2750/2 = 1375.
Since 10% of 1375 = 137.5, and 4*(137.5) = 550, the simple interest rate is 40%.
Compounded annually, Shawn will get 20% the first year, 20% the second year.
Amount at end of the first year = 1375 + 275 = 2650.
Interest second year = .2 * 2650 = 330. Success!
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