romitvsingh 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?
$ 2750
$ 5500
$ 11000
$ 22000
$ 44000
I've included the answer choices, which would be provided by the GMAT.
For both bonds, the first-year interest is the same:
550/2 = 275.
In the second year, the additional interest earned by the compound interest bond = 605-550 = 55.
This additional interest occurs because the interest rate was applied to the 275 earned in the first year.
Thus, the interest rate for the second year = 55/275 * 100 = 20%.
Since 20% is earned each year, the simple interest rate over 2 years = 40%.
Thus, 40% of 1/2 of the correct answer choice must yield simple interest of 550.
Only answer choice
A works:
.4*(1/2)*2750 = 550.
The correct answer is
A.
Alternatively, once we've determined the simple interest rate, we could use algebra:
.4(.5)x = 550
x = 550/.2 = 2750.
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