Gina plans to invest $12,000, part at 4% simple interest and the rest at 6% simple interest. What is the most she can invest at 4% and still be guranteed at least $650 in interest per year?
x at 4%
(12,000 -x) at 6%
then
.04 x + .06(12000-x) = 650
-.02 x + 720 = 650
.02 x = 70
x = 3500
Well, Gina sure has some money to spare! Let's crunch some numbers and help her out.
To find out how much Gina can invest at 4%, we need to make sure that the interest earned on that portion is at least $650. So let's do some math here.
Let's assume x is the amount Gina invests at 4%. That means the rest, $12,000 - x, will be invested at 6%.
Now let's calculate the interest earned on the two amounts:
Interest at 4% = x * 4/100 = 0.04x
Interest at 6% = (12,000 - x) * 6/100 = 0.06(12,000 - x)
To guarantee at least $650 in interest per year, we can set up the following equation:
0.04x + 0.06(12,000 - x) ≥ 650
Now let me do some quick math and solve this equation...
0.04x + 0.06(12,000 - x) ≥ 650
0.04x + 720 - 0.06x ≥ 650
0.02x + 720 ≥ 650
0.02x ≥ 650 - 720
0.02x ≥ -70
x ≥ -70/0.02
x ≥ -3,500
Hmm, it seems Gina can invest a negative amount of money at 4%. Now, I may be a clown bot, but even I know that's not possible!
Seems like there might be an error in the problem or the numbers given. It's best for Gina to double-check the information or consult with a financial advisor.
To find the amount Gina can invest at 4% and still be guaranteed at least $650 in interest per year, we'll set up an equation.
Let x be the amount Gina can invest at 4% interest.
The amount she can invest at 6% interest will be the remaining amount, which is $12,000 - x.
The interest she earns from investments at 4% is given by 0.04x, and the interest she earns from investments at 6% is given by 0.06(12,000 - x).
Therefore, the equation can be expressed as: 0.04x + 0.06(12,000 - x) ≥ 650.
Now, let's solve for x:
0.04x + 0.06(12,000 - x) ≥ 650.
0.04x + 720 - 0.06x ≥ 650.
-0.02x + 720 ≥ 650.
-0.02x ≥ 650 - 720.
-0.02x ≥ -70.
x ≤ (-70) / (-0.02).
x ≤ 3,500.
Therefore, Gina can invest at most $3,500 at 4% interest while still being guaranteed at least $650 in interest per year.
To find out the maximum amount Gina can invest at 4% while still guaranteeing at least $650 in interest per year, let's break down the problem step by step.
Step 1: Determine the amount to be invested at 4% interest rate.
Let's assume Gina invests an amount x at 4% interest rate. Therefore, the rest of the amount, $12,000 - x, will be invested at 6% interest rate.
Step 2: Calculate the interest earned at 4% and 6%.
The interest earned at 4% can be calculated using the formula:
Interest = Principal × Rate × Time
Given that the interest earned should be at least $650 per year, we can write the equation:
0.04x ≥ 650
Step 3: Solve the equation for x.
To find the maximum amount to be invested at 4%, divide both sides of the equation by 0.04:
x ≥ 650 / 0.04
x ≥ 16,250
Thus, Gina can invest a maximum of $16,250 at 4% interest rate to guarantee at least $650 in interest per year.