To solve the problem, we need to determine the value of Pierce's money five years ago, given that he currently has [tex]$10,000 and has earned 5 percent interest annually. We'll use the formula for the present value:
\[
\text{Present Value} = \frac{\text{Future Value}}{(1+i)^t}
\]
where:
- Future Value (FV) = $[/tex]10,000
- Annual Interest Rate (i) = 5% or 0.05
- Number of Years (t) = 5
Step-by-Step Solution:
1. Identify the given values:
- Future Value (FV) = [tex]\( 10,000 \)[/tex]
- Interest Rate (i) = [tex]\( 0.05 \)[/tex]
- Time (t) = [tex]\( 5 \)[/tex] years
2. Apply the formula for the present value:
[tex]\[
\text{Present Value} = \frac{10,000}{(1 + 0.05)^5}
\][/tex]
3. Calculate the denominator:
[tex]\[
(1 + 0.05)^5 = 1.05^5
\][/tex]
- Raise 1.05 to the power of 5.
4. Perform the division:
[tex]\[
\text{Present Value} = \frac{10,000}{(1.05^5)}
\][/tex]
5. Evaluate the numerical value:
- Evaluating the division gives us:
[tex]\[
\frac{10,000}{(1.05)^5} \approx 7,835.26
\][/tex]
Therefore, from the given options, the correct answer for the value of Pierce's money five years ago is:
[tex]\[
\boxed{7{,}835.26}
\][/tex]
So, the answer is B. $7,835.26.
