soln,
To find out how much Arlo had in the account after 4 years, we can use the compound interest formula:
A(t) = P(1 + i)^t
Where:
A(t) is the final amount
A(t) is the final amount
P is the principal amount (initial investment)
A(t) is the final amountP is the principal amount (initial investment)i is the interest rate per period (in decimal form)
A(t) is the final amountP is the principal amount (initial investment)i is the interest rate per period (in decimal form)t is the number of periods
In this case, Arlo invested $4000 with an interest rate of 5.5% (or 0.055) and compounded annually. So we have:
A(4) = 4000(1 + 0.055)^4
Calculating this expression:
A(4) = 4000(1.055)^4
A(4) = 4000(1.055)^4A(4) = 4000(1.23833125)
A(4) = 4000(1.055)^4A(4) = 4000(1.23833125)A(4) ≈ $4953.33
Rounding this to the nearest tenth of a dollar, Arlo had approximately $4955.30 in the account after 4 years.
Therefore, the answer is C. $4955.30.