A chartered bank offers a five-year Escalator Guaranteed Investment Certificate (GIC) that pays annual interest rates of 4%, 4.5%, 5%, 5.5%, and 6% in successive years, compounded at the end of each year. It also offers a regular five-year GIC paying a fixed rate of 5% compounded annually. What is the maturity value of $1000 invested in the regular five-year 5% GIC (so that you can compare it with the escalator GIC)?

Introduction / Context:
This question compares two investment products: an Escalator GIC with changing annual interest rates and a regular GIC with a constant rate. To compare them, it is useful to know the exact maturity value of the regular five-year 5% GIC on a $1000 investment. This highlights how average rates and compounding interact in real financial products.

Given Data / Assumptions:

• Principal P = $1000
• Regular GIC rate r = 5% per annum
• Time T = 5 years
• Compounding annually
• Escalator GIC rates (for comparison) are 4%, 4.5%, 5%, 5.5%, and 6% per year, but the numeric answer sought is the maturity value of the regular GIC

Concept / Approach:
For the regular GIC, the same 5% rate applies every year. The amount after 5 years with annual compounding is:
A = P * (1 + r / 100)^TAfter we find this amount, we can qualitatively compare it with the escalator GIC, whose maturity value is very close but slightly lower than that of the regular GIC.

Step-by-Step Solution:
Step 1: Use the compound amount formula.A = 1000 * (1 + 5 / 100)^5Step 2: Simplify the factor.1 + 5 / 100 = 1.05Step 3: Compute (1.05)^5.(1.05)^2 = 1.1025(1.05)^3 ≈ 1.157625(1.05)^4 ≈ 1.21550625(1.05)^5 ≈ 1.27628156Step 4: Multiply by the principal.A ≈ 1000 * 1.27628156 ≈ $1276.28

Verification / Alternative check:
If we also compute the maturity of the Escalator GIC: A ≈ 1000 * 1.04 * 1.045 * 1.05 * 1.055 * 1.06 ≈ $1276.14. This is very close to, but slightly less than, $1276.28. This confirms that a constant 5% rate over 5 years yields almost the same result as the average of the given escalating rates.

Why Other Options Are Wrong:
$1234 and $1256: These underestimate the growth at 5% over five years.$1278 and $1260: These are approximations that do not match the precisely calculated compound amount for 5 years at 5%.

Common Pitfalls:
Students sometimes average the rates and multiply principal by (1 + 0.05 * 5) as if interest were simple, forgetting about compounding. Others may miscalculate (1.05)^5 by rounding too early. Always apply the compound interest formula correctly and keep adequate precision until the final step.

Final Answer:
The maturity value of $1000 invested in the regular five-year GIC paying 5% compounded annually is $1276.28.