A four year Guaranteed Investment Certificate (GIC) has a principal of 9000 dollars and earns a nominal interest rate of 5.25% per annum compounded monthly. If the investor receives monthly interest payments only and the principal is repaid at maturity, what is the amount of each monthly interest payment?

Introduction / Context:
This question focuses on calculating the periodic interest amount paid on an investment when interest is paid out regularly rather than reinvested. Such products, like GICs or fixed deposits with interest payout, are common, and understanding how to compute the monthly interest is an important basic financial skill.

Given Data / Assumptions:

• Principal amount P = 9000 dollars.
• Nominal annual interest rate j = 5.25% per annum.
• Interest is compounded monthly, so there are 12 compounding periods per year.
• Only the interest is paid out every month; the principal is returned at the end of four years.
• We must find the monthly interest payment.

Concept / Approach:
If only interest is paid every month and the principal is not reduced, then each month the investor simply receives P multiplied by the monthly interest rate i, where i = j / 12. The monthly interest payment remains the same throughout the investment period, because the principal does not change. This is different from an amortizing loan or an annuity, where the principal is gradually repaid.

Step-by-Step Solution:
Step 1: Compute the monthly interest rate i = j / 12.Step 2: j = 5.25% per annum, so i = 5.25% / 12.Step 3: Numerically, 5.25% is 0.0525 as a decimal, so i = 0.0525 / 12.Step 4: i = 0.004375 per month, which is 0.4375% per month.Step 5: The monthly interest payment is P * i = 9000 * 0.004375.Step 6: 9000 * 0.004375 = 39.375, which rounds to 39.38 dollars per month.

Verification / Alternative check:
As a check, convert the monthly interest back to an annual amount. A monthly interest of about 39.38 dollars on 9000 dollars implies a yearly interest of roughly 39.38 * 12 = 472.56 dollars. Dividing 472.56 by 9000 gives 0.0525, which is 5.25%. This confirms that the monthly payment is consistent with the nominal annual rate of 5.25% per annum.

Why Other Options Are Wrong:

• 29.38: This corresponds to a lower monthly rate than 5.25% per annum and would not match the given nominal rate.
• 49.38: This implies an annual interest rate higher than 5.25% when multiplied by 12.
• 59.38: This would lead to an even higher annual rate, far above the stated 5.25% per annum.

Common Pitfalls:
Some learners mistakenly treat this as an annuity problem and try to compute a payment that includes both interest and principal, which is not what the question describes. Others forget to convert the annual nominal rate into a monthly rate by dividing by 12, and instead use 5.25% directly as the monthly rate, which produces an unrealistically large payment. Careful reading of the wording about interest only payments is essential.

Final Answer:
The investor will receive a monthly interest payment of approximately 39.38 dollars each month for the four year period.