Calculate the future value of an investment of $3000 placed at 7% annual interest for 5 years, if the interest is compounded annually.

Introduction / Context:
This question is a direct application of the compound interest formula to find the future value of an investment. The principal, annual rate, number of years, and compounding frequency are all clearly given. Such problems are fundamental in finance because they show how a lump sum grows over time when interest is reinvested, and they are frequently used to illustrate the power of compounding.

Given Data / Assumptions:

• Principal P = 3000 dollars
• Annual rate of interest r = 7% per annum
• Time n = 5 years
• Interest is compounded once per year
• We need to find the future value A

Concept / Approach:
With annual compounding, the future value A of a principal P invested at rate r for n years is given by A = P * (1 + r)^n, where r is expressed in decimal form. Because the compounding is annual, we do not need to adjust the rate or the number of periods beyond the given values. Once we calculate the factor (1.07)^5, we multiply it by the principal to obtain the final amount. Careful multiplication or the use of a scientific calculator yields an accurate value.

Step-by-Step Solution:
P = 3000, r = 7% = 0.07, n = 5 years Formula: A = P * (1 + r)^n A = 3000 * (1 + 0.07)^5 A = 3000 * 1.07^5 Compute 1.07^5 step by step: 1.07^2 = 1.1449 1.07^3 = 1.1449 * 1.07 ≈ 1.2250 1.07^4 = 1.2250 * 1.07 ≈ 1.3108 1.07^5 = 1.3108 * 1.07 ≈ 1.4026 A ≈ 3000 * 1.4026 ≈ 4207.8, which rounds to 4207.66 using more precise values

Verification / Alternative check:
Using a calculator directly for 1.07^5 gives approximately 1.402552. Multiplying this by 3000 yields 4207.656, which rounds to 4207.66. This matches the given option exactly. The result also makes sense because the amount must be somewhat more than 3000 plus five simple interest periods of 7% each, and 5 * 0.07 = 0.35, so a simple estimate would be around 3000 * 1.35 = 4050. Because of compounding, the true value should be higher than 4050, and 4207.66 fits that expectation.

Why Other Options Are Wrong:
5207, 4376, and 5687 are all significantly larger than the expected range based on simple and compound growth at 7% for 5 years. None of these values are close to 4207.66 when you compute the exact factor, so they do not represent the correct future value for this investment.

Common Pitfalls:
Some learners mistakenly multiply by 1.07 only once instead of raising it to the fifth power, effectively computing only one year of growth. Others treat 7% as 0.7 in decimal form, which is off by a factor of ten and leads to wildly incorrect answers. Careful attention to the percent to decimal conversion and to the exponent on the growth factor is crucial.

Final Answer:
The future value of the 3000 dollar investment at 7 percent per annum compounded annually for 5 years is $4207.66.