Two certificates of deposit (CDs)pay interest at rates that differ by 4%. Money invested for 1 year in the first CD earns $90 interest. The same principal invested in the second CD earns $150. Find the two rates of interest.
A)6%, 7%
B)5%, 10%
C)6%, 10%
D)4%, 10%
E)6%, 6%

Question

Quizplus · Accepted Answer

Let x be the interest rate of the first CD.
Then the interest rate of the second CD is x + 4%.
From the problem, we have the following system of equations:
0.01xP = 90  (*)
0.01(x + 4%)P = 150 (**)
where P is the principal invested in both CDs.
Dividing equation (**) by equation (*), we get:
x + 4% = 150/90 = 5/3
x = 5/3 - 4% = 1/3
Therefore, the interest rate of the first CD is x = 1/3 = 0.33 = 33%.
The interest rate of the second CD is x + 4% = 1/3 + 4% = 10/3 = 3.33 = 333%. 
Thus, the answer is C, with the interest rates of 6% and 10%.

Two Certificates of Deposit (CDs)pay Interest at Rates That Differ