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On January 1 of the current year, Lean Co. made an investment of [tex]$\$[/tex]10,000[tex]$. The following is the present value of $[/tex]\[tex]$1.00$[/tex] discounted at a [tex]$10\%$[/tex] interest rate.

[tex]\[
\begin{array}{ll}
\text{Periods} & \text{Present value of } \$1.00 \text{ discounted at } 10\% \\
1 & 0.909 \\
2 & 0.826 \\
3 & 0.751 \\
\end{array}
\][/tex]

What amount of cash will Lean accumulate in two years?

A. [tex]$\$[/tex]12,000[tex]$

B. $[/tex]\[tex]$12,107$[/tex]

C. [tex]$\$[/tex]16,250[tex]$

D. $[/tex]\[tex]$27,002$[/tex]



Answer :

GinnyAnswer
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

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