An investor buys a four-year, monthly-payment Guaranteed Investment Certificate (GIC) with a principal of $9000 that earns a nominal interest rate of 5.25% per annum, compounded monthly. If the investor receives equal monthly interest cheques (and the principal is repaid only at maturity), what fixed periodic payment will the investor receive each month?

Introduction / Context:
This question comes from financial mathematics and focuses on a common investment product: a monthly-payment Guaranteed Investment Certificate (GIC). In such a GIC, the investor typically receives regular interest payments while the principal (original deposit) remains intact and is returned at maturity. We must determine the monthly interest payment from a $9000 deposit earning a nominal 5.25% per annum compounded monthly.

Given Data / Assumptions:

Principal (deposit) P = $9000
Nominal annual interest rate = 5.25% per annum
Compounding frequency = monthly (12 times per year)
Term = 4 years, but principal is not amortized; it is returned at the end
Monthly payment is interest only, based on the monthly periodic rate

Concept / Approach:
For an interest-only investment with monthly payments, the periodic payment equals the principal multiplied by the periodic interest rate. The nominal annual rate must be converted to a monthly rate by dividing by 12. Since the principal is not being repaid during the term, we do not use annuity formulas. We simply compute the monthly interest and treat that as the periodic payment.

Step-by-Step Solution:
Step 1: Find the monthly periodic rate. Monthly rate i = 5.25% / 12 = 0.0525 / 12. i = 0.004375 per month (which is 0.4375%). Step 2: Compute the monthly interest payment. Monthly payment = P * i = 9000 * 0.004375. Monthly payment = 39.375 dollars. Step 3: Round to two decimal places. Monthly payment ≈ $39.38.

Verification / Alternative check:
If the investor receives $39.38 each month for 12 months, the total interest in one year is approximately 39.38 * 12 ≈ 472.56 dollars. The simple interest at 5.25% on $9000 for one year is 9000 * 0.0525 = 472.50 dollars. The slight difference is due to rounding the monthly payment to two decimal places, which confirms that $39.38 is a consistent and accurate monthly interest cheque amount.

Why Other Options Are Wrong:
A payment of $29.38 or $49.38 would correspond to considerably lower or higher effective rates than 5.25% per annum. A payment of $59.38 would imply an unrealistically high annual return on $9000. Only $39.38 aligns with the correct monthly rate of 0.4375% and produces a reasonable annual total close to 5.25% of the principal.

Common Pitfalls:
A frequent error is to misinterpret the problem as an amortizing annuity, using formulas that include repayment of principal. Another mistake is to forget to divide the nominal annual rate by 12 to obtain the monthly rate. Always check whether principal is being repaid over time or only at maturity, because that completely changes the calculation method.

Final Answer:
The investor will receive a fixed monthly interest payment of approximately $39.38.