Question

Your friend makes a comment about how expensive the baseball card pack was that he purchased. He says 10 years ago he could buy a pack of baseball cards for $5. Assuming inflation is 3%, compunded continuously, how much did he pay for the pack today?

Round your answers to the nearest cent (hundredth).

Answer 1

$6.75

Explanation:

In order to calculate the cost of the baseball card pack today, taking into account 3% continuous compounding inflation over 10 years, we can use the formula for continuously compounded interest:

`\sf A=\ P \cdot e^(rt)`

Where:

• A is the final amount (the cost today)
• P is the initial amount (the cost 10 years ago)
• r is the annual inflation rate (3% or 0.03 as a decimal)
• t is the number of years (10 years)

In this case:

• P = $5
• r = 0.03
• t = 10

Substitute these values into the formula and simplify:

`\begin{aligned} \textsf{ Final Value (A) } & = \$ 5 \cdot e^(0.03 \cdot 10) \\\\ &= \$ 5 \cdot e^(0.3) \\\\ & = \$ 5 \cdot 1.349858808 \\\\ &= \$ 6.749294038\\\\ &= \$ 6.75 \textsf{ in nearest cent(hundred )}\end{aligned}`

0ur friend paid approximately $6.75 for the pack of baseball cards today.