Final answer:
To replace a piece of equipment that costs $30,000 today and will have a salvage value of $7,000 after ten years, accounting for a 6% inflation rate and a 4% investment interest rate, an engineer should set aside approximately $4,207 annually over the ten-year period.
Step-by-step explanation:
The question at hand involves calculating how much money needs to be set aside each year to replace a piece of equipment after ten years, taking into account inflation and the interest rate on investments. The cost of the new equipment will be adjusted for inflation, while the savings to fund it will grow at the interest rate.
To calculate the future cost of the equipment, we use the formula for future value with inflation: Future Value = Present Value * (1 + Inflation Rate)Number of Years. The present value is $30,000, and the inflation rate is 6%. After 10 years, the future cost of the equipment is: $30,000 * (1 + 0.06)10 = $53,820.23, approximately.
We subtract the salvage value of $7,000 from this amount, resulting in $46,820.23. This is the amount that needs to be saved up over 10 years.
To find out the annual installment, we use the formula for the present value of an annuity: Present Value of Annuity = Payment * [(1 - (1 + Interest Rate)-Number of Payments) / Interest Rate]. Rearranging the formula to solve for the payment gives us the annual installment that needs to be set aside. Solving this for the given interest rate of 4% over 10 years gives us:
Payment = $46,820.23 * [0.04 / (1 - (1 + 0.04)-10)]
Payment ≈ $4,207
Hence, the engineer should set aside approximately $4,207 each year to replace the equipment after ten years.