What is the present worth of a safety improvement benefit of $5,000 set to occur in 5 years at an interest rate of 4%?

To determine the present worth of a future benefit, you need to calculate the present value (PV) of that future amount using the formula for present value:

[ PV = \frac{FV}{(1 + r)^n} ]

where:

• ( FV ) is the future value (in this case, the safety improvement benefit of $5,000),

• ( r ) is the interest rate (0.04 for 4%),

• ( n ) is the number of years until the benefit is realized (5 years).

Plugging the values into the formula, we have:

[ PV = \frac{5000}{(1 + 0.04)^5} ]

Calculating the denominator:

[ (1 + 0.04)^5 = 1.04^5 \approx 1.2167 ]

Now substituting back into the present value formula gives:

[ PV \approx \frac{5000}{1.2167} \approx 4,110.62 ]

So, the present worth of the safety improvement benefit is approximately $4,110.62, which when rounded is $4,110. This calculation accurately reflects how the time value of money affects the