Final answer:
To solve the problem, first find the interest rate from the initial deposit scenario and then use that rate to determine the interest from the new deposit. After calculating, the resultant interest matches one of the given options.
Step-by-step explanation:
To determine how much annual interest is received on a deposit of $13,090.00 at the same rate as a previous deposit which earned an annual interest of $551.25 from a $10,500.00 deposit, we use the concept of proportional relationships. The interest received is directly proportional to the amount deposited, assuming the interest rate and the time period remain constant.
Firstly, we should find the interest rate earned by the initial deposit. We can express this rate (R) as:
R = Interest / Principal
For the first deposit, this is calculated as follows:
R = $551.25 / $10,500.00
After calculating the rate, we can then apply this rate to find the interest earned on the new deposit amount:
I = R × New principal
Plugging the values we know:
I = ($551.25 / $10,500.00) × $13,090.00
After performing the calculation, we find the interest I that would be earned on a $13,090.00 deposit. The correct answer matches one of the provided options: a) $676.95, b) $720.25, c) $813.45, or d) $935.70.