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Bunuel
Simple interest on a certain sum for 3 years at 8% per annum is equal to half the compound interest on $4000 for 2 years at 10% per annum. What is the sum placed on simple interest?

A. $840
B. $1250
C. $1550
D. $1750
E. $1950
Solution:

Let’s find the compound interest first. The interest for the first year of a $4000 investment at 10% per annum is 4000 x 0.1 = $400. The interest for the second year is (4000 + 400) x 0.1 = $440 (due to compounding interest). Therefore, for the $4000 investment, the total interest for the two years is 400 + 440 = $840. Half that value is $420.

We can now calculate the amount placed in simple interest. We can let p = the principal for 3 years at 8% per annum in simple interest and create the equation:

p x 8/100 x 3 = 420

p x 6/25 = 420

p = 420 x 25/6 = 70 x 25 = $1750

Answer: D
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