Question

Two certificates of deposit pay interest at rates that differ by 2%. Money invested for one year in the first CD earns $300 interest. The same principal invested in the other CD earns $400. Find the two rates of interest.

Answer 1

The two rates are 6% and 8%

Explanation:

Call the two rates r1 and r2. Call p the principal. Write down the problem as an equation system:

`p\cdot r_1 = 300\\p \cdot r_2 = 400\\r_2-r_1 = 0.02`

which are 3 equations with 3 unknowns, so they can be solved. I first divide the two equations to get:

`p\cdot r_1 = 300\\p \cdot r_2 = 400\\\implies r_1 = (3)/(4)r_2`

and use that in the third:

`r_2-r_1 = 0.02\\r_2-(3)/(4)r_2=0.02\\r_2=0.08 \implies r_1=0.06`

The two rates are 6% and 8%