Answer-first summary for fast verification
Answer: $142,442.
The correct answer is **B** because the present value (PV) of the annuity due (payments at the beginning of each year) 10 years from today is calculated as follows: - **Step 1**: Calculate the PV of the annuity due: $$PV_{10} = \$50,000 + \$50,000 \times \left[1 - \frac{1}{(1.03)^3}\right]/0.03 = \$50,000 + \$50,000 \times 2.828611 = \$191,431.$$ - **Step 2**: Discount this amount back to today (PV₀): $$PV_0 = \frac{\$191,431}{(1.03)^{10}} = \$142,442.$$ Alternatively, treating the annuity as an ordinary annuity (payments at the end of each year) with a PV 9 years from today: - **Step 1**: Calculate the PV of the ordinary annuity: $$PV_9 = \$50,000 \times \left[1 - \frac{1}{(1.03)^4}\right]/0.03 = \$50,000 \times 3.717098 = \$185,855.$$ - **Step 2**: Discount this amount back to today (PV₀): $$PV_0 = \frac{\$185,855}{(1.03)^9}} = \$142,442.$$ Both methods yield the same result, confirming the correctness of **B**.
Author: LeetQuiz Editorial Team
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An investor must cover college tuition fees starting in 10 years. The annual fee is $50,000, payable at the beginning of each year for 4 years. If the investor's annual discount rate is 3%, the minimum investment required today to fund all four years of tuition is closest to:
A
$138,294.
B
$142,442.
C
$146,716.
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