The function C(t)=C"_"0(1+r)^t models the rise in the cost of a product that has a cost of C"_"0 today, subject to an average yearly inflation rate of r for t years.  If the average annual rate of inflation over the next 8 years is assumed to be 1.5%, what will the inflation-adjusted cost of a $169 bicycle be in 8 years?  Round to two decimal places.

To determine the inflation-adjusted cost of a $169 bicycle in 8 years with an average annual inflation rate of 1.5%, we use the given function:

\[ C(t) = C_0 (1 + r)^t \]

Where:
- $ C_0 = 169 $ (the current cost of the bicycle)
- $ r = 0.015 $ (the annual inflation rate, converted to a decimal)
- $ t = 8 $ (the number of years)

Plugging in the values, we get:

\[ C(8) = 169 \times (1 + 0.015)^8 \]

First, calculate $ 1 + r $:

\[ 1 + r = 1 + 0.015 = 1.015 \]

Next, raise $ 1.015 $ to the power of 8:

\[ 1.015^8 \approx 1.1268 \]

Now, multiply this result by the initial cost $ C_0 $:

\[ C(8) = 169 \times 1.1268 \approx 190.43 \]

So, the inflation-adjusted cost of the bicycle in 8 years will be approximately $190.43.

Do you want more details or have any questions?

Here are some related questions to further your understanding:
1. What is the formula used for calculating compound interest?
2. How would the cost change if the inflation rate was 2% instead of 1.5%?
3. How does inflation impact purchasing power over time?
4. Can you derive the formula for continuous compounding?
5. What is the difference between nominal and real interest rates?
6. How would you calculate the future cost if the inflation rate changes each year?
7. What other factors, besides inflation, could affect the cost of a product over time?
8. How can understanding inflation help in financial planning?

**Tip:** Always convert percentage rates to decimal form before using them in mathematical calculations.

Explore how to calculate the inflation-adjusted cost of a $169 bicycle over 8 years with a 1.5% average annual inflation rate. This problem covers compound interest concepts and uses the compound interest formula. Suitable for Grades 10-12 students and anyone interested in financial mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation