Question

Two certificates of deposit pay interest at rates that differ by 4%. Money invested for one year in the first CD earns $175 interest. The same principal invested in the other CD earns $275. Find the two rates of interest.

a) 5%, 9%
b) 8%, 12%
c) 7%, 11%
d) 6%, 10%

Answer 1

The interest rates of the two CDs are 7% and 11%, calculated by solving for the lower rate r and using the equation Interest = Principal x Rate with a difference of 4% between the two rates.

Step-by-step explanation:

The question asks us to find the two rates of interest for certificates of deposit (CDs) that differ by 4%, where the first CD earns $175 in interest, and the other earns $275 with the same principal for one year. To solve this, let's denote the lower interest rate as r and the higher interest rate as r + 4%. The interest earned on a CD can be calculated using the formula Interest = Principal x Rate. Since the principal is the same for both CDs, we can set up the following equations:

• Principal x r = $175
• Principal x (r + 4%) = $275

We can divide the second equation by the first to eliminate the principal and solve for r:

(r + 4%) / r = $275 / $175

Solving for r gives us r = 7%. Therefore, the two CD rates are 7% and 11%, that is option