Final answer:
To find the minimum amount to justify a wire transfer, we calculate the interest lost due to the two-day delay of an ACH transfer. With an annual interest rate of 3%, the difference in transfer cost is equivalent to the interest on $153,314 over two days, making that the minimum amount to justify a wire transfer.
Step-by-step explanation:
The question is asking for the minimum amount of money that justifies using a wire transfer over an ACH transfer, given the overnight investment rate and costs for each method. To solve for this, we need to calculate the opportunity cost of the two-day delay for the ACH transfer in terms of the interest that could have been earned during those two days if the wire transfer was used.
Since the annual interest rate is 3%, the daily interest rate is 3% divided by 365 days, which equals approximately 0.008219% per day. Over two days, the interest rate would be double that, or 0.016438%. The cost difference between wire and ACH transfers is $26 - $0.80 = $25.20. The minimum amount that justifies the wire transfer would when this cost difference is equal to the interest earned over two days by using the wire transfer.
Let x be the minimum amount, then:
x * 0.00016438 = $25.20,
x = $25.20 / 0.00016438,
x ≈ $153,313.66.
So, the minimum amount needed to justify using the wire transfer, rounded to the nearest whole dollar, is $153,314.