To estimate the price of the car at the end of 5 years, we will use the formula for compound interest, since the price of the car is expected to increase by a certain percentage each year.
The formula for compound interest is:
A = P(1 + r)^n
Where:
A = Final amount (price of the car at the end of 5 years)
P = Initial amount (current price of the car)
r = Interest rate per year (as a decimal)
n = Number of years
Now let's calculate the answers to your questions:
a. Estimate the price of the car at the end of 5 years if inflation is:
1. 2% per year:
Given:
P = $14,000 (current price)
r = 2% or 0.02
n = 5 (number of years)
Plugging these values into the formula:
A = $14,000(1 + 0.02)^5
A โ $15,637.13
Therefore, if inflation is 2% per year, the estimated price of the car at the end of 5 years will be around $15,637.13.
2. 4% per year:
Given:
P = $14,000 (current price)
r = 4% or 0.04
n = 5 (number of years)
Plugging these values into the formula:
A = $14,000(1 + 0.04)^5
A โ $16,494.27
Therefore, if inflation is 4% per year, the estimated price of the car at the end of 5 years will be around $16,494.27.
b. To find out how much more expensive the car will be if the rate of inflation is 4% rather than 2%, we need to calculate the difference between the estimated prices in both cases.
Difference = Price at 4% - Price at 2%
Difference = $16,494.27 - $15,637.13
Difference โ $857.14
Therefore, the car will be approximately $857.14 more expensive if the rate of inflation is 4% rather than 2%.