Answer: $125,779.

## Explanation This is a **future value of an ordinary annuity** problem. An ordinary annuity has payments made at the **end** of each period, which matches the description "the first contribution is made one year from today." ### Formula: The future value of an ordinary annuity is calculated as: \[ FV = PMT \times \frac{(1 + r)^n - 1}{r} \] Where: - \( PMT = \$10,000 \) (annual payment) - \( r = 0.05 \) (annual interest rate) - \( n = 10 \) (number of payments) ### Calculation: \[ FV = 10,000 \times \frac{(1.05)^{10} - 1}{0.05} \] First, calculate \( (1.05)^{10} \): \[ (1.05)^{10} \approx 1.628894626777 \] Then: \[ (1.05)^{10} - 1 = 0.628894626777 \] Divide by \( r = 0.05 \): \[ \frac{0.628894626777}{0.05} = 12.57789253554 \] Multiply by \( PMT = 10,000 \): \[ FV = 10,000 \times 12.57789253554 = 125,778.9253554 \] Rounding to the nearest dollar gives approximately **$125,779**. ### Why the other options are incorrect: - **Option B ($132,068)**: This might result from incorrectly using an annuity due formula (payments at the beginning of each period) or miscalculating the interest factor. - **Option C ($142,068)**: This could result from compounding errors or using the wrong formula entirely. **Key Concept**: This question tests understanding of time value of money concepts, specifically the future value of an ordinary annuity. The critical distinction is recognizing that payments are made at the end of each period (ordinary annuity) rather than at the beginning (annuity due).

Author: LeetQuiz .