Michael invested a certain amount of money at 3% interest and $750 more than that amount at 5%. His total yearly interest was $157.50. How much did he invest at each rate?
Po*0.03*1 + (Po+750)*0.05*1 = 157.50.
0.03Po + 0.05Po + 37.50 = 157.50,
0.08Po = 120, Po = $1500 @ 3%.
1500 + 750 = $2250 @ 5%.
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Let's assume that Michael invested x dollars at 3% interest.
The amount he invested at 5% interest would be x + $750, since it is $750 more than the amount he invested at 3%.
The interest earned from the investment at 3% would be 0.03x (3% of x dollars).
The interest earned from the investment at 5% would be 0.05(x + $750) (5% of (x + $750) dollars).
According to the given information, the total yearly interest earned was $157.50. So we can write the equation:
0.03x + 0.05(x + $750) = $157.50
Now, let's solve this equation step-by-step:
0.03x + 0.05(x + $750) = $157.50
0.03x + 0.05x + 0.05($750) = $157.50
0.03x + 0.05x + 0.05($750) = $157.50
0.03x + 0.05x + 0.05 * 750 = 157.50
0.03x + 0.05x + 37.50 = 157.50
0.08x + 37.50 = 157.50
0.08x = 157.50 - 37.50
0.08x = 120.00
x = 120.00 / 0.08
x = 1500.00
Therefore, Michael invested $1500 at 3% interest and $1500 + $750 = $2250 at 5% interest.
To solve this problem, we can set up a system of equations. Let's represent the amount invested at 3% as x.
Given that the amount invested at 5% is $750 more than the amount invested at 3%, we can say that the amount invested at 5% is (x + $750).
Now, we can use the formula for calculating simple interest: Interest = Principal × Rate × Time.
The formula for calculating the yearly interest at 3% is: 0.03x.
The formula for calculating the yearly interest at 5% is: 0.05 * (x + $750).
According to the problem, the total yearly interest is $157.50. Therefore, we can set up the equation:
0.03x + 0.05(x + $750) = $157.50
Now, let's solve this equation step by step:
0.03x + 0.05x + 0.05($750) = $157.50
0.08x + 0.05($750) = $157.50
0.08x + $37.50 = $157.50
0.08x = $157.50 - $37.50
0.08x = $120
To solve for x, we'll divide both sides of the equation by 0.08:
x = $120 / 0.08
x = $1500
Therefore, Michael invested $1500 at 3% interest.
To find the amount invested at 5% interest, we can substitute the value we just found into the equation we set up earlier:
Amount invested at 5% = x + $750 = $1500 + $750 = $2250
Therefore, Michael invested $1500 at a rate of 3% and $2250 at a rate of 5%.