To determine how much the car will cost in 7 years given an initial cost and a compounded annual inflation rate, we can use the compound interest formula. The formula to calculate the future cost with compound interest is:
[tex]\[ A = P (1 + r)^n \][/tex]
Where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial cost of the car).
- [tex]\( r \)[/tex] is the annual interest rate (inflation rate in this case).
- [tex]\( n \)[/tex] is the number of years the money is invested or borrowed for.
Given:
- The initial cost of the car [tex]\( P = 400,000 \)[/tex] units of currency.
- The annual inflation rate [tex]\( r = 11\% = 0.11 \)[/tex] (as a decimal).
- The number of years [tex]\( n = 7 \)[/tex].
Using the formula:
[tex]\[ A = 400,000 \times (1 + 0.11)^7 \][/tex]
First, calculate [tex]\( 1 + 0.11 \)[/tex]:
[tex]\[ 1 + 0.11 = 1.11 \][/tex]
Next, raise this to the power of 7:
[tex]\[ 1.11^7 \approx 2.076563 \][/tex]
Now, multiply this result by the initial cost of the car:
[tex]\[ 400,000 \times 2.076563 \approx 830,464.06 \][/tex]
Therefore, the car will cost approximately:
[tex]\[ \boxed{830,464.06} \][/tex]
after 7 years, considering the inflation rate of 11% compounded annually.
