To determine the final amount in a savings account that earns simple interest, we use the formula:
[tex]\[ A = P + I \][/tex]
where:
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( I \)[/tex] is the interest earned over a period of time.
Simple interest can be calculated using the formula:
[tex]\[ I = P \cdot r \cdot t \][/tex]
where:
- [tex]\( I \)[/tex] is the simple interest,
- [tex]\( P \)[/tex] is the principal amount,
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal),
- [tex]\( t \)[/tex] is the time the money is invested for, in years.
Given the problem:
- The principal amount [tex]\( P \)[/tex] is \$200,
- The annual interest rate [tex]\( r \)[/tex] is [tex]\(3.75\% = 0.0375\)[/tex] (as a decimal),
- The time [tex]\( t \)[/tex] is 6 years.
First, we calculate the simple interest [tex]\( I \)[/tex]:
[tex]\[ I = 200 \cdot 0.0375 \cdot 6 = 45 \][/tex]
Next, we determine the final amount [tex]\( A \)[/tex]:
[tex]\[ A = 200 + 45 = 245 \][/tex]
Therefore, the correct formula to determine the final amount is:
[tex]\[ A = (200)(0.0375)(6) + 200 \][/tex]
This matches the third option in the list:
[tex]\[ A = (200)(0.0375)(6) + 200 \][/tex]
