Question

To improve crack detection in aircraft, the U.S. Air Force combined ultrasonic in- spection procedures with laser heating to identify fatigue cracks. Early detection of cracks may reduce repair costs by as much as $200.000 per year. What is the present worth of these savings over a 5-year pe- riod at an interest rate of 10% per year?

Answer 1

The present worth of the savings over a 5-year period at an interest rate of 10% per year is $803,965.20.

Step-by-step explanation:

To calculate the present worth of savings over a 5-year period, we need to use the formula for present worth:

PW = (Savings per year) × (1 - (1 + interest rate)^-n) / interest rate

In this case, the savings per year is $200,000, the interest rate is 10% (or 0.10), and the number of years is 5. Plugging these values into the formula, we get:

PW = (200,000) × (1 - (1 + 0.10)^-5) / 0.10 = $803,965.20

Therefore, the present worth of these savings over a 5-year period at an interest rate of 10% per year is $803,965.20.