had is planning to buy a rototiller next spring at an expected price of $579. In the current fall "flyer" from Evergreen Lawn and Garden, the model he wants is advertised at $499.95 in a Fall Clearance Special.

c. What interest rate would money have to earn for Thad to be indifferent between buying the rototiller at $499.95 on September 15 or buying it for $579 on the subsequent April 1?

To find the interest rate at which Thad would be indifferent between buying the rototiller now (September 15) for $499.95 or waiting until April 1 to buy it for $579, we can use the concept of future value (FV) in finance.

The idea is that if Thad invests the $499.95 on September 15 at a certain interest rate, it should grow to exactly $579 by April 1. We need to solve for the interest rate that makes this true.

### Steps:

1. **Present Value (PV)**: This is the current price, $499.95.
2. **Future Value (FV)**: This is the future price, $579.
3. **Time Period**: We need to calculate the time between September 15 and April 1. That’s 6.5 months, or approximately $ \frac{6.5}{12} = 0.5417 $ years.
4. **Interest Rate Formula**: 
   \[
   FV = PV \times (1 + r)^{t}
   \]
   where:
   - $ FV = 579 $
   - $ PV = 499.95 $
   - $ t = 0.5417 $ (the time in years)
   - $ r $ is the annual interest rate we need to find.

Rearrange the formula to solve for $ r $:
\[
r = \left( \frac{FV}{PV} \right)^{\frac{1}{t}} - 1
\]

Let's now calculate the interest rate.The interest rate that money would have to earn for Thad to be indifferent between buying the rototiller at $499.95 on September 15 or buying it for $579 on April 1 is approximately **31.13% per year**.

Would you like more details on the calculation or further clarification?

Here are five related questions to consider:
1. What are the typical interest rates for savings accounts or investments?
2. How could Thad find an investment with a 31.13% return?
3. What are the risks of waiting for a higher future price versus buying now at a discount?
4. How would the calculation change if the time period were different (e.g., 9 months)?
5. How would inflation impact the decision to buy now or later?

**Tip**: When comparing costs over time, always consider the time value of money and potential interest you could earn!

Thad is planning to buy a rototiller next spring at an expected price of $579. In the current fall 'flyer' from Evergreen Lawn and Garden, the model he wants is advertised at $499.95 in a Fall Clearance Special. What interest rate would money have to earn for Thad to be indifferent between buying the rototiller at $499.95 on September 15 or buying it for $579 on the subsequent April 1?

Learn how to calculate the interest rate at which a present value of $499.95 grows to $579 over a period of 6.5 months. This example covers key financial concepts like future value, time value of money, and interest rate formulas, suitable for high school to college-level students.

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