To determine the amount of Mr. Murphy's inheritance given that he earned [tex]$4500 in interest over 5 years at an interest rate of 3.6%, we can use the simple interest formula:
\[
I = P \times R \times T
\]
Where:
- \( I \) is the interest earned,
- \( P \) is the principal amount (the initial amount of inheritance),
- \( R \) is the annual interest rate (expressed as a decimal),
- \( T \) is the time period the money is invested for (in years).
Given:
- \( I = \$[/tex]4500 \),
- [tex]\( R = 3.6\% = 0.036 \)[/tex] (converted to decimal form),
- [tex]\( T = 5 \)[/tex] years.
We need to solve for [tex]\( P \)[/tex] (the principal). Rearrange the formula to solve for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{I}{R \times T}
\][/tex]
Substitute the given values into the formula:
[tex]\[
P = \frac{4500}{0.036 \times 5}
\][/tex]
Calculate the denominator first:
[tex]\[
0.036 \times 5 = 0.18
\][/tex]
Now, divide the interest earned by this result:
[tex]\[
P = \frac{4500}{0.18}
\][/tex]
Perform the division:
[tex]\[
P = 25000
\][/tex]
Therefore, Mr. Murphy's inheritance was \$25,000.
