Final answer:
To find the quarterly interest rate necessary to grow $1635 to $1748.73 over 2.25 years, we used the compound interest formula and determined that the rate needed is 3.00% quarterly.
Step-by-step explanation:
To calculate the quarterly interest rate needed for an investment of $1635 to grow to $1748.73 after 2.25 years, we use the formula for compound interest:
A = P(1 + r/n)(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount ($1635 in this case)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the time the money is invested or borrowed for, in years (2.25 years in this case)
Since we are looking for the quarterly interest rate, n will be 4 (since there are 4 quarters in a year). We can now plug in the values and solve for r:
1748.73 = 1635(1 + r/4)(4 * 2.25)
After solving for r, we find that the correct quarterly interest rate is Option C, 3.00%.