An investor can place $1000 in a regular five year guaranteed investment certificate that pays a fixed rate of 5% per annum, compounded annually. What maturity value will the $1000 grow to after 5 years in this 5% annual GIC?

Introduction / Context:
This question asks for the maturity value of an investment in a guaranteed investment certificate (GIC) that pays a fixed annual interest rate and compounds annually. This is a standard compound interest problem but phrased in the context of a common financial product. Understanding how to compute such maturity values helps investors compare fixed income options and forecast future balances of safe investments.

Given Data / Assumptions:

• Principal P = 1000 dollars
• Annual interest rate r = 5% per annum
• Time period n = 5 years
• Interest is compounded annually at the end of each year
• We must find the maturity value A of the regular 5% GIC

Concept / Approach:
Under annual compounding, the maturity amount A is given by the classic compound interest formula A = P * (1 + r)^n. Here, r = 0.05 and n = 5. The calculation involves raising 1.05 to the fifth power and multiplying by the principal. This is a direct application with no intermediate cash flows or rate changes, making it an excellent example of base time value of money principles.

Step-by-Step Solution:
P = 1000, r = 5% = 0.05, n = 5 years Formula: A = P * (1 + r)^n A = 1000 * (1 + 0.05)^5 A = 1000 * 1.05^5 Compute the power 1.05^5: 1.05^2 = 1.1025 1.05^3 = 1.1025 * 1.05 ≈ 1.1576 1.05^4 = 1.1576 * 1.05 ≈ 1.2155 1.05^5 = 1.2155 * 1.05 ≈ 1.2763 A ≈ 1000 * 1.2763 ≈ 1276.28 (using more precise values)

Verification / Alternative check:
Using a more precise calculator value, 1.05^5 is about 1.2762816. Multiplying by 1000 gives 1276.2816, which rounds to 1276.28. This matches the option provided. This value is slightly larger than what simple interest would give (which would be 1000 * (1 + 5 * 0.05) = 1250), reflecting the effect of compounding each year. Therefore, the maturity value is consistent with both the formula and intuitive expectations for a 5% investment over 5 years.

Why Other Options Are Wrong:
1234 and 1256 are both smaller than the correct compound maturity value and could correspond to lower interest rates or shorter periods. 1278 is slightly higher than 1276.28 and does not match the precise calculation from the formula. Only 1276.28 is consistent with a 5% annual compound rate over 5 years on 1000 dollars.

Common Pitfalls:
Some candidates confuse simple and compound interest and compute 1000 + 5% of 1000 * 5 instead of applying the compound factor. Others mistakenly use 1.5 instead of 1.05 in the formula by misreading 5% as 50%. Careful reading of the rate and correct conversion of percentage to decimal form are vital for accurate results.

Final Answer:
The maturity value of the 1000 dollar investment in the 5 percent annual GIC after 5 years is $1276.28.