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Answer :
To find the interest earned on Ed Bland's savings, we use the simple interest formula:
[tex]\[ I = P \times r \times t \][/tex]
where:
- [tex]\( I \)[/tex] is the interest,
- [tex]\( P \)[/tex] is the principal amount (initial savings),
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal),
- [tex]\( t \)[/tex] is the time in years.
Let's break down the calculation step-by-step:
1. Identify the principal (P):
The principal amount, [tex]\( P \)[/tex], is \[tex]$837.
2. Convert the interest rate to a decimal (r):
The interest rate is given as \(4 \frac{1}{2}\%\) which is equivalent to \(4.5\%\).
To convert to a decimal, divide by 100:
\[
r = \frac{4.5}{100} = 0.045
\]
3. Determine the time in years (t):
The time, \( t \), is 3 years.
4. Calculate the simple interest (I):
Substitute the values into the formula:
\[
I = 837 \times 0.045 \times 3
\]
5. Multiply to find the interest:
\[
I = 837 \times 0.045 \times 3 = 112.995
\]
6. Round the interest to the nearest cent:
The interest rounded to the nearest cent is \$[/tex]113.00.
Therefore, the interest earned on Ed Bland's savings is \$113.00.
[tex]\[ I = P \times r \times t \][/tex]
where:
- [tex]\( I \)[/tex] is the interest,
- [tex]\( P \)[/tex] is the principal amount (initial savings),
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal),
- [tex]\( t \)[/tex] is the time in years.
Let's break down the calculation step-by-step:
1. Identify the principal (P):
The principal amount, [tex]\( P \)[/tex], is \[tex]$837.
2. Convert the interest rate to a decimal (r):
The interest rate is given as \(4 \frac{1}{2}\%\) which is equivalent to \(4.5\%\).
To convert to a decimal, divide by 100:
\[
r = \frac{4.5}{100} = 0.045
\]
3. Determine the time in years (t):
The time, \( t \), is 3 years.
4. Calculate the simple interest (I):
Substitute the values into the formula:
\[
I = 837 \times 0.045 \times 3
\]
5. Multiply to find the interest:
\[
I = 837 \times 0.045 \times 3 = 112.995
\]
6. Round the interest to the nearest cent:
The interest rounded to the nearest cent is \$[/tex]113.00.
Therefore, the interest earned on Ed Bland's savings is \$113.00.
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