An amount of $3,300 is required in 4 years at an interest rate of 11% per annum compounded annually. What is the amount of interest earned over 4 years (that is, the difference between the future value and the present value)?

Introduction:
This question is about finding the present value and then the interest earned when a future amount of 3,300 dollars is needed in 4 years at a compound interest rate of 11% per annum. The key step is to discount the future value back to today and then subtract the present value from the future value to obtain the total interest earned over the period.

Given Data / Assumptions:

• Future value, A = 3,300 dollars (amount needed after 4 years)
• Annual interest rate, r = 11% per annum
• Compounding frequency: annually
• Number of years, n = 4
• We want the interest earned, which equals A minus the present value P

Concept / Approach:
For compound interest, the relationship between present value P and future value A is: A = P * (1 + r)^n To find P from A, we rearrange: P = A / (1 + r)^n Once P is known, the total interest I earned is: I = A - P

Step-by-Step Solution:
Step 1: Convert the interest rate from percent to decimal. r = 11% = 0.11 Step 2: Compute the discount factor (1 + r)^n. (1 + r)^4 = (1.11)^4 (1.11)^2 ≈ 1.2321 (1.11)^4 ≈ 1.2321 * 1.2321 ≈ 1.5187 Step 3: Calculate the present value P. P = 3300 / 1.5187 ≈ 2173.81 dollars Step 4: Compute the interest earned I. I = A - P = 3300 - 2173.81 ≈ 1126.19 dollars Step 5: Round to two decimal places. I ≈ 1126.19 dollars

Verification / Alternative check:
We can verify by computing forward from the present value: A = 2173.81 * (1.11)^4 ≈ 2173.81 * 1.5187 ≈ 3300 The small differences are due to rounding, but the result confirms that a present value of about 2173.81 dollars grows to about 3,300 dollars in 4 years. The difference between these amounts, 1126.19 dollars, is the total interest earned.

Why Other Options Are Wrong:
1237.00: This overestimates the interest and does not match the correct discounting calculation. 2863.00: This is almost the entire future value and cannot be the amount of interest alone. 1892.00: This is also too large to be only the interest earned for an 11% rate over 4 years. 956.19: This underestimates the interest; it might come from mistaken use of simple interest or a wrong exponent. 1126.19: This matches the precise calculation using the compound interest relationship between present and future values.

Common Pitfalls:
A common mistake is to calculate simple interest using I = P * r * n, which does not apply here because the question is about compound interest. Another error is forgetting to discount the future value and instead multiplying incorrectly by (1 + r)^n. Careless rounding before subtracting can also slightly distort the value of the interest, so it is important to maintain precision until the final step.

Final Answer:
The interest earned over 4 years, when a future amount of 3,300 dollars is required at 11% per annum compounded annually, is approximately 1126.19 dollars.