An amount of 3,300 dollars is needed in 4 years at an interest rate of 11% per annum compounded annually. What is the total interest earned over the 4 year period?

Introduction / Context:
This question combines the concepts of present value, future value, and total interest earned under compound interest. You know the amount required in the future and the interest rate, and you must compute how much of that future amount is interest rather than original principal.

Given Data / Assumptions:

• Future value A = 3,300 dollars (amount needed after 4 years).
• Annual interest rate r = 11% per annum, compounded yearly.
• Time period n = 4 years.
• Interest is compounded annually with no additional deposits during the period.

Concept / Approach:
First find the present value P that will grow to 3,300 dollars at 11% in 4 years using:
A = P * (1 + r)^n Rearrange to find P:
P = A / (1 + r)^n The total interest earned is then:
Interest = A - P

Step-by-Step Solution:
Step 1: Convert 11% to decimal form: r = 0.11. Step 2: Compute the discount factor (1 + r)^4 = 1.11^4. Step 3: Calculate P = 3300 / (1.11^4) ≈ 2,173.81 dollars. Step 4: Compute interest earned: Interest = 3300 - 2173.81 ≈ 1,126.19 dollars. Therefore the interest earned over 4 years is approximately 1,126.19 dollars.

Verification / Alternative Check:
You can grow the present value forward to check. Multiply 2,173.81 dollars by 1.11 four times. The result will be very close to 3,300 dollars, which confirms that the calculations for present value and interest are correct.

Why Other Options Are Wrong:
Option B (1,050.00 dollars) and option D (1,000.00 dollars) underestimate the interest, which would correspond to a lower effective rate or a shorter time period.
Option C (1,237.00 dollars) overestimates the interest compared with the correct compound interest computation.
Option E is incorrect because one of the numerical options matches the correct interest value precisely.

Common Pitfalls:
Students may mistakenly calculate simple interest using P * r * n instead of compound interest, or they may treat 3,300 dollars as the principal. It is crucial to distinguish between future value and present value and to remember that interest is the difference between them.

Final Answer:
The total compound interest earned over the 4 year period is 1,126.19 dollars.