To solve for the future cost of the motorcycle given the initial cost, the annual inflation rate, and the number of years, we will use the compound interest formula [tex]\( C(t) = C_0(1 + r)^t \)[/tex].
Let's break down the steps:
1. Identify the given values:
- The initial cost [tex]\( C_0 \)[/tex] is \[tex]$27,000.
- The annual inflation rate \( r \) is 3.5%. Converting this to a decimal, \( r = \frac{3.5}{100} = 0.035 \).
- The number of years \( t \) is 13.
2. Substitute the values into the formula:
\[
C(t) = 27000 \times (1 + 0.035)^{13}
\]
3. Calculate the base inside the exponent:
\[
1 + 0.035 = 1.035
\]
4. Raise the base to the power of 13:
\[
1.035^{13}
\]
5. Multiply the result by 27,000:
\[
C(t) = 27000 \times 1.035^{13}
\]
6. Calculate the final value and round it to two decimal places:
After performing these calculations, the result is:
\[
C(t) \approx 42226.81
\]
Therefore, the inflation-adjusted cost of the motorcycle in 13 years is approximately \$[/tex]42,226.81 when rounded to two decimal places.
