Explanation:
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.
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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.