Certainly! To find out how much Greg initially invested (the Principal), we can use the formula for Simple Interest. The formula for simple interest is:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
We need to solve for the Principal, so we will isolate the Principal on one side of the equation. Let's rearrange the formula to solve for Principal:
Starting with the original formula:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Dividing both sides of the equation by \(\text{Rate} \times \text{Time}\):
[tex]\[ \text{Principal} = \frac{\text{Interest}}{\text{Rate} \times \text{Time}} \][/tex]
This formula now allows us to find the Principal (the amount Greg initially invested) in terms of the known variables: Interest, Rate, and Time.
#### Given the values:
- Interest earned: \$1200
- Rate (in decimal): 0.12
- Time: 10 years
You would plug these values into the rearranged formula to find the Principal as:
[tex]\[ \text{Principal} = \frac{1200}{0.12 \times 10} \][/tex]
Simplifying the calculation:
[tex]\[ \text{Principal} = \frac{1200}{1.2} \][/tex]
[tex]\[ \text{Principal} = 1000 \][/tex]
Therefore, Greg initially invested \$1000.
