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Question 2 of 6

After 8 years, Susan's account earned [tex]$\[tex]$1500$[/tex][/tex] in interest. If the interest rate (in decimal form) is 0.1, how much did Susan initially invest?

\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{Susan's Bank Statement} \\
\hline Interest Earned & [tex]$\[tex]$1500$[/tex][/tex] \\
\hline Rate & 0.1 \\
\hline Time & 8 Years \\
\hline Principal Invested & [tex]$?$[/tex] \\
\hline
\end{tabular}

Without substitution, solve the formula for the unknown variable in terms of the known variables.



Answer :

GinnyAnswer
To determine how much Susan initially invested, we need to start with the formula for simple interest:

[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]

We are given the interest earned, the interest rate, and the time period. We need to solve this formula for the unknown variable, which is the principal amount that Susan initially invested. Let's isolate the principal (P) in the formula.

1. Write down the formula for simple interest:
[tex]\[ I = P \times R \times T \][/tex]

2. We need to solve for \( P \). To do that, let's divide both sides of the equation by \( R \times T \):
[tex]\[ P = \frac{I}{R \times T} \][/tex]

So, the formula for the principal in terms of the interest, rate, and time is:

[tex]\[ P = \frac{I}{R \times T} \][/tex]

This formula allows us to find the initial investment (principal) by dividing the interest earned by the product of the rate and time.

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