Chartered Financial Analyst Level 1

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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.

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.

Comments (1)

H YoonJun 9, 2026 7:15 AM

10년 후부터, 4년동안 매해 초에 냄(t=10~13). 그걸 t=1에 몰아서 내는 거임. (연금이랑 비슷) t=10 기준 PV= =50,000(1+0.97087+0.94260+0.91514) = 191,431 t=1 기준 PV0=(191,431) / (1.03)^10 = 142,XXX

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:

Exam-Like

Last updated: July 15, 2026 at 14:06

$138,294.

14.3%

$142,442.

71.4%

$146,716.

14.3%

Chartered Financial Analyst Level 1

Comments (1)

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:

Comments (1)

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: