If Mark invests $8000 at 6% simple interest rate, how much money must he invest at an 8% simple interest rate in order for the interest on each investment to be $500. Assume that the amount of time for both investments is the same.
500=8000*.06+M*.08
solve for M.
2500
To find the amount of money Mark must invest at an 8% simple interest rate, we can use the formula for simple interest:
Interest = Principal (amount of money invested) * Rate * Time
Let's break down the problem.
For the first investment, Mark invests $8000 at a 6% simple interest rate. The interest earned on this investment is $500.
So, we can write the equation as:
500 = 8000 * 0.06 * Time
To find the time, we divide both sides of the equation by (8000 * 0.06):
500 / (8000 * 0.06) = Time
Time ≈ 1.042
Now that we know the time, we can use it to find out how much money Mark should invest at an 8% interest rate to earn $500 in interest.
The equation becomes:
500 = Principal * 0.08 * 1.042
To find the principal, we divide both sides by (0.08 * 1.042):
500 / (0.08 * 1.042) = Principal
Principal ≈ $6,048.08
Therefore, Mark must invest approximately $6,048.08 at an 8% simple interest rate to earn $500 in interest.