To determine how much Arlo had in the account after 4 years, we use the compound interest formula:
[tex]\[ A = P(1 + i)^t \][/tex]
where:
- [tex]\( A \)[/tex] is the amount of money in the account after [tex]\( t \)[/tex] years,
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( i \)[/tex] is the annual interest rate (as a decimal),
- [tex]\( t \)[/tex] is the number of years the money is invested.
Given:
- [tex]\( P = \$ 4000 \)[/tex],
- [tex]\( i = 5.5\% = 0.055 \)[/tex],
- [tex]\( t = 4 \)[/tex] years.
Substituting the given values into the formula, we get:
[tex]\[ A = 4000 \times (1 + 0.055)^4 \][/tex]
This calculation results in:
[tex]\[ A = 4000 \times (1.055)^4 \][/tex]
After performing the calculations, we find:
[tex]\[ A \approx 4955.30 \][/tex]
Therefore, after 4 years, Arlo had approximately \[tex]$4955.30 in the account.
Thus, the correct answer is:
C. $[/tex]\[tex]$ 4955.30$[/tex]
