The annual inflation rate is 3.1% per year. If a movie ticket costs $10.50 today, find a formula for f the price of a movie ticket t years from today, assuming that movie tickets keep up with inflation.
final amount = (start amount) [1 + (growth per period)]^(number of periods)
f = $10.50 (1 + .031)^t
this technique also works for compound interest
3.1% = .031
1 + .031 = ?
f = $10.5 * (?^t)
To find a formula for the price of a movie ticket t years from today, assuming that movie tickets keep up with inflation, we can use the formula for compound interest.
The formula for compound interest is:
A = P * (1 + r)^n
Where:
A = the final amount (price of a movie ticket t years from today)
P = the initial amount (current price of the movie ticket)
r = the interest rate per compounding period (annual inflation rate)
n = the number of compounding periods (number of years)
In this case, the initial amount (P) is $10.50, the interest rate (r) is 3.1% per year (or 0.031), and the number of years (n) is t.
Therefore, the formula for the price of a movie ticket t years from today would be:
A = $10.50 * (1 + 0.031)^t
Simplifying further:
A = $10.50 * (1.031)^t
So, the formula for the price of a movie ticket t years from today, assuming that movie tickets keep up with inflation, is A = $10.50 * (1.031)^t.
To find the formula for the price of a movie ticket t years from today, we need to account for the annual inflation rate.
The formula for calculating the future price after t years can be derived using compound interest formula:
Future Value = Present Value * (1 + r)^t
Where:
- Future Value is the price of a movie ticket t years from today
- Present Value is the current price of a movie ticket ($10.50 in this case)
- r is the annual inflation rate expressed as a decimal (3.1% = 0.031)
- t is the number of years in the future
Substituting the given values into the formula:
Future Value = $10.50 * (1 + 0.031)^t
This formula will give you the price of a movie ticket t years from today, taking into account the annual inflation rate.