Final answer:
Using the compound interest formula, Arnold's ending balance after one year would be approximately $4,250.52, which is not listed among the given options, indicating a possible error in the options or a rounding issue.
Step-by-step explanation:
To calculate the ending balance of an investment with compound interest, we use the formula A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In Arnold's case, the principal P is $4,200, the annual interest rate r is 1.18% or 0.0118 in decimal form, n is compounded weekly so 52 times per year, and t is 1 year. Plugging these values into the formula gives A = $4,200(1 + 0.0118/52)52*1.
Calculating this out, we get Arnold's ending balance after one year which is A ≈ $4,250.5202. The closest answer to this calculation is $4,250.52, which is not explicitly listed in the options provided. However, it appears there may be a slight error in the provided options or a rounding difference.