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Question 2 of 6, Step 2 of 3

After 10 years, Greg's account earned [tex]$\$[/tex]1200$ in interest. If the interest rate (in decimal form) is 0.12, how much did Greg initially invest?

\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{Greg's Bank Statement} \\
\hline Interest Earned & [tex]$\$[/tex]1200$ \\
\hline Rate & 0.12 \\
\hline Time & 10 Years \\
\hline Principal Invested & [tex]$?$[/tex] \\
\hline
\end{tabular}

Step 2 of 3: Without substitution, solve the formula for the unknown variable in terms of the known variables.



Answer :

GinnyAnswer
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.

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