Present worth at compound interest Compute the present worth of $220.50 due in 2 years at 5% per annum compounded annually.

Introduction / Context:Unlike simple interest, compound interest grows the amount by applying the rate to the current balance each compounding period. Present worth is the amount today that would accumulate to the due sum under compounding.

Given Data / Assumptions:

• Future amount S = $220.50.
• Time t = 2 years.
• Annual compound interest rate i = 5%.

Concept / Approach:Present worth PW = S / (1 + i)^t. This inverts the compound-amount formula S = PW * (1 + i)^t.

Step-by-Step Solution:(1 + i)^t = 1.05^2 = 1.1025.PW = 220.50 / 1.1025 = $200.00.

Verification / Alternative check:Forward check: $200 * 1.1025 = $220.50, confirming the present worth exactly equals $200.

Why Other Options Are Wrong:$197.5, $202, and $192.25 do not satisfy the exact compounding relationship with S = $220.50 at 5% for 2 years.

Common Pitfalls:Using simple-interest discounting for a compound-interest question or miscomputing 1.05^2. Always observe whether the problem states “compound” or “simple.”

Final Answer:$ 200