To determine the amount of cash that Lean Co. will accumulate in two years from an initial investment of \[tex]$10,000, given a present value of \$[/tex]1.00 discounted at 10% over 2 periods (years), we can follow these steps:
1. Understand the Present Value Factor: Given the present value table, we see that the present value of \[tex]$1 discounted at 10% for 2 years is 0.826. This means that \$[/tex]1 in today's terms is equivalent to \[tex]$0.826 two years from now when discounted at an annual rate of 10%.
2. Set up the Problem: We know that the present value (PV) of the future amount (FV) after 2 years is \$[/tex]10,000, and the present value factor (PV factor) for 2 years at 10% interest is 0.826.
3. Rearrange the Present Value Formula to find Future Value:
[tex]\[
FV = \frac{PV}{\text{PV factor}}
\][/tex]
4. Substitute the given values into the formula and solve:
[tex]\[
FV = \frac{\$10,000}{0.826}
\][/tex]
5. Calculate:
[tex]\[
FV = 10,000 \div 0.826 \approx 12,106.54
\][/tex]
Thus, Lean Co. will accumulate approximately \[tex]$12,106.54 in two years.
Therefore, the correct answer is:
B. \$[/tex]12,107
