To compute the amount of interest earned for a deposit of \[tex]$7,500 at an annual interest rate of 6.5% for 120 days using simple interest, we can follow these steps:
1. Identify the Principal Amount (P):
The principal amount is the initial amount of money deposited, which is \$[/tex]7,500.
2. Identify the Annual Interest Rate (r):
The annual interest rate is given as 6.5%. To use this in calculations, it needs to be converted into its decimal form. Therefore,
[tex]\[
r = \frac{6.5}{100} = 0.065
\][/tex]
3. Identify the Time Period (t):
The time period for which the interest is to be calculated is given in days. Here, it is 120 days. To convert this into years, recognizing that there are 365 days in a year, we calculate:
[tex]\[
t = \frac{120}{365} \approx 0.3288 \text{ years}
\][/tex]
4. Formula for Simple Interest (I):
The formula for calculating simple interest is:
[tex]\[
I = P \times r \times t
\][/tex]
5. Substitute the Values into the Formula:
Insert the principal, annual interest rate as a decimal, and time in years into the formula:
[tex]\[
I = 7500 \times 0.065 \times 0.3288
\][/tex]
6. Calculate the Interest:
Performing the multiplication:
[tex]\[
I \approx 7500 \times 0.065 \times 0.3288 = 160.27397260273972
\][/tex]
So, the amount of interest earned on a deposit of \[tex]$7,500 at an annual interest rate of 6.5% for 120 days is approximately \$[/tex]160.27.
