Interest Rate Calculation for Tires Purchase

How many years will the premium tires have to last for them to be as economically attractive as the all-season tires at an interest rate of 10% per year?

Assuming you drive 10,000 miles per year, what is the breakeven point for the premium tires compared to the all-season tires?

The premium tires will have to last for years, and the spreadsheet function to find the breakeven point is

The breakeven point can be found using logarithmic functions in a spreadsheet. The formula would be "=LOG($260.79/$125)/LOG(1.10)".

To calculate the breakeven point, we need to determine how many years the premium tires would have to last for their cost to be economically equivalent to the all-season tires.

Let's break down the calculation step by step:

Step 1:

Calculate the total cost of the all-season tires over the expected lifespan:

Total cost of all-season tires = Cost per tire * Number of tires = $94 * 4 = $376

Step 2:

Determine the present value of the cost of the all-season tires at an interest rate of 10% per year, assuming a 30,000-mile lifespan:

Present value of all-season tires = Total cost of all-season tires / (1 + Interest rate)^(Lifespan / Miles driven per year)

Present value of all-season tires = $376 / (1 + 0.10)^(30,000 / 10,000) = $376 / (1.10)^3 = $260.79

Step 3:

Determine how many years the premium tires would need to last to have a present value cost equivalent to the all-season tires:

Breakeven years = Log(Present value of all-season tires / Cost per premium tire) / Log(1 + Interest rate)

Breakeven years = Log($260.79 / $125) / Log(1.10) ≈ 1.97 years

Therefore, the premium tires would need to last approximately 1.97 years (or rounded up to 2 years) to be as economically attractive as the all-season tires at an interest rate of 10% per year.