If the inflation rate averages, 3% per year compounded annually for the next 5 years, what will the car currently selling for $17,000 cost 5 years from now?
17000*1.03^5
To calculate the future cost of the car after 5 years, we need to account for the inflation rate of 3% per year compounded annually.
To do this step-by-step:
Step 1: Calculate the future value factor:
The future value factor can be calculated using the formula:
Future Value Factor = (1 + Inflation Rate)^Number of Years
In this case, the inflation rate is 3% and the number of years is 5.
Future Value Factor = (1 + 0.03)^5 = 1.159274
(rounded to six decimal places)
Step 2: Calculate the future cost of the car:
To find the future cost, we multiply the current cost of the car ($17,000) by the future value factor:
Future Cost = Current Cost x Future Value Factor
Future Cost = $17,000 x 1.159274
Future Cost = $19,730.48
(rounded to two decimal places)
Therefore, the car will cost approximately $19,730.48 in 5 years if the inflation rate averages 3% per year compounded annually.
To calculate the cost of the car 5 years from now, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the car
P = the current value of the car ($17,000)
r = the annual interest rate (3% or 0.03)
n = the number of times the interest is compounded per year (compounded annually)
t = the number of years (5)
Plugging in the values:
A = 17000(1 + 0.03/1)^(1*5)
A = 17000(1 + 0.03)^5
A = 17000(1.03)^5
Using a calculator:
A ≈ 17000(1.159274) ≈ $19,699.45
Therefore, the car will cost approximately $19,699.45 after 5 years at an average inflation rate of 3% per year compounded annually.