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What is the quarterly interest rate that you will need to earn in order for an investment of $1635 to grow to be $1748.73 after 2.25 years?

A. 8.93%
B. 13.93%
C. 12.93%
D. 3.00%
E. 10.93%

User Bcattle
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1 Answer

3 votes

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%.

User Withtaker
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