Final answer:
To find the balance in Frank's account after eight years, we can use the formula for compound interest. Frank will have contributed $5600 to the total balance of his account after eight years. The interest earned can be calculated by subtracting the contributions made by Frank from the total balance.
Step-by-step explanation:
To find the balance in Frank's account after eight years, we can use the formula for compound interest. We know that Ali makes deposits of $175 at the beginning of every three months, and the interest earned is 4.5% compounded quarterly. To calculate the future balance, we can use the formula A = P(1 + r/n)^(nt), where A is the balance, P is the principal (initial deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values, we have:
A = 175[(1 + 0.045/4)^(4 * 8)]
To calculate how much of the balance Frank will have contributed, we can multiply the deposit amount by the number of deposits made in eight years. Since Ali makes deposits of $175 every three months, the number of deposits in eight years would be 8 * 4 = 32. Therefore, Frank will have contributed $175 * 32 = $5600.
The amount of the balance that is interest can be calculated by subtracting the contributions made by Frank from the total balance. So, the interest would be $A - $5600.