Question

An engineer is tasked with determining the annual amount to set aside to replace a piece of equipment costing $30,000 today with an identical model in ten years. Given a salvage value of $7,000 after ten years, inflation at 6%, and an effective annual interest rate of 4%, calculate the required yearly savings.

Answer 1

To calculate the required yearly savings, we need to find the future value of the equipment's cost after 10 years and then subtract the salvage value. Required yearly savings = ($54,660 - $7,000) / 10 = $4,766

Step-by-step explanation:

To calculate the required yearly savings, we need to find the future value of the equipment's cost after 10 years and then subtract the salvage value. This can be done using the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)^n

Where:

• Present Value = $30,000
• Interest Rate = (1 + Inflation Rate) * (1 + Interest Rate) - 1 = (1 + 0.06) * (1 + 0.04) - 1 = 1.1 * 1.04 - 1 = 0.144
• n = 10 years

Using these values in the formula:

Future Value = $30,000 * (1 + 0.144)^10 = $30,000 * 1.822 = $54,660

Required yearly savings = (Future Value - Salvage Value) / n = ($54,660 - $7,000) / 10 = $47,660 / 10 = $4,766