Given the following data, use present worth analysis

to find the best alternative, A,B, or C.
A B C
Initial cost $10,000 15,000 $12,000
Annual benefit 6,000 10,000 5,000
Salvage value 1,000 −2,000 3,000
Useful life 2 years 3 years 4 years
Use an analysis period of 12 years and 10% interest.

The formula I have for this question is:
6000(P/A,10%,2)+1000(P/F,10%,2)-10,000

Where do I add in the analysis period (12 years)??

To determine the best alternative using present worth analysis, you need to calculate the present worth of each alternative and choose the one with the highest present worth. The formula you provided is a good starting point, but we need to incorporate the analysis period of 12 years.

The present worth of an alternative can be calculated using the following formula:

PW = (Annual benefit)(P/A, i%, n) + (Salvage value)(P/F, i%, n) - Initial cost

Where:
- PW is the present worth of the alternative
- Annual benefit is the net cash flow for each year
- (P/A, i%, n) is the present worth factor for an annual series of cash flows over n years at an interest rate of i%
- Salvage value is the future value of the investment at the end of its useful life
- (P/F, i%, n) is the present worth factor for a single cash flow at the end of n years at an interest rate of i%
- Initial cost is the initial investment required for the alternative

Now, let's calculate the present worth for each alternative:

For alternative A:
PW_A = (6000)(P/A, 10%, 2) + (1000)(P/F, 10%, 2) - 10000

For alternative B:
PW_B = (10000)(P/A, 10%, 2) + (-2000)(P/F, 10%, 2) - 15000

For alternative C:
PW_C = (5000)(P/A, 10%, 4) + (3000)(P/F, 10%, 4) - 12000

Note that for alternative C, the salvage value and useful life are 3 years and 4 years, respectively. So, we need to adjust the present worth factor accordingly.

To take into account the analysis period of 12 years, you would compare the 12-year present worth of each alternative. Calculate the present worth using the formulas above and choose the alternative with the highest present worth value.