Question

a bowling ball costs $100 today and the inflation rate is 4%. how much will a bowling ball cost in 15 years assuming continuous compounding? round your answer to the nearest cent (hundredth).

Explanation:

Step1: Recall the formula for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount (initial cost), $r$ is the annual interest rate (inflation rate in decimal), $t$ is the time in years, and $e$ is the base of the natural logarithm.
Here, $P = 100$, $r = 0.04$ (since 4% = 0.04), and $t = 15$.

Step2: Substitute the values into the formula

Substitute $P = 100$, $r = 0.04$, and $t = 15$ into $A = Pe^{rt}$:
$A = 100 \times e^{0.04 \times 15}$

Step3: Calculate the exponent

First, calculate $0.04 \times 15 = 0.6$.

Step4: Calculate the value of $e^{0.6}$

Using a calculator, $e^{0.6} \approx 1.82211880039$.

Step5: Calculate the final amount

Multiply 100 by the value of $e^{0.6}$:
$A = 100 \times 1.82211880039 \approx 182.21$

Answer:

$\$182.21$