Final answer:
The correct answer is option B) 3.2% and 2.6%. By setting up equations using the simple interest formula and the given information, we find the interest rates for the two investments by isolating the variable representing the interest rate.
Step-by-step explanation:
The correct answer is option B) 3.2% and 2.6%. To determine the interest rates, we can set up two equations based on the given information. Let the interest rate of the $8,000 investment be r, and since the $15,000 is invested at a rate 0.6% higher, its interest rate will be r + 0.6%. Using the formula for simple interest (I = Prt), where I is the interest, P is the principal, r is the rate, and t is time, we have:
- $15,000 × (r + 0.6%) - $8,000 × r = $685
Assuming the investments are for the same time period, we can ignore the time factor as it would cancel out. Simplifying the equation, we get:
- $150 × r + $90 - $80 × r = $685
- $70 × r + $90 = $685
- $70 × r = $685 - $90
- $70 × r = $595
- r = $595 / $70
- r = 8.5%
However, since the rates are given in percentages, we must convert this decimal rate back to a percentage by multiplying by 100:
Which means the interest rate for the $8,000 investment is 8.5% (or 2.6% as a percentage of the principal). The rate for the $15,000 investment is then:
- r + 0.6% = 2.6% + 0.6% = 3.2%