Jan plans to invest $7500, part at 4% simple interest and the rest at 5% simple interest. What is the most that he can invest at 4% and still be guaranteed at least $325 per year?

part at 4% --- x

part at 5% --- 7500-x

.04x + .05(7500-x) = 325
after you multiply each term by 100 to get rid of the decimals this is an easy equation to solve.
Go for it.

To find the most that Jan can invest at 4% and still be guaranteed at least $325 per year, we can set up an equation using the formula for simple interest: Interest = Principal × Rate × Time.

Let's assume Jan invests an amount x at 4% interest. So, the interest earned from this amount is given by 0.04x (4% is equivalent to 0.04 as a decimal).

The remaining amount that Jan invests (7500 - x) will be invested at 5% interest, and the interest earned from this amount is given by 0.05(7500 - x).

The total interest earned should be at least $325. So, we can set up the equation:

0.04x + 0.05(7500 - x) ≥ 325

Now, let's solve this equation to find the maximum value for x.

0.04x + 0.05(7500 - x) ≥ 325
0.04x + 375 - 0.05x ≥ 325
0.01x ≥ 325 - 375
0.01x ≥ -50
x ≥ -50 / 0.01
x ≥ 5000

Therefore, the most Jan can invest at 4% and still be guaranteed at least $325 per year is $5000.