Answer-first summary for fast verification
Answer: $4,767,427.
The correct answer is **A** because the present value (PV) is calculated using the formula: \[ PV = FV \times (1 + \frac{r}{m})^{-N \times m} \] Where: - \( FV = \$10,000,000 \) (future value) - \( r = 5\% \) (annual interest rate) - \( m = 2 \) (compounding periods per year) - \( N = 15 \) (number of years) Substituting the values: \[ PV = \$10,000,000 \times (1 + \frac{0.05}{2})^{-15 \times 2} = \$4,767,426.85 \approx \$4,767,427 \] Alternatively, using a financial calculator in **END mode**: - \( N = 30 \) (total compounding periods) - \( I/Y = 2.5\% \) (periodic rate) - \( PMT = 0 \) - \( FV = \$10,000,000 \) - Compute \( PV = \$4,767,427 \). **Option B** is incorrect as it uses the annual rate (5%) without adjusting for semi-annual compounding. **Option C** is incorrect due to a miscalculation of the compounding factor and periods.
Author: LeetQuiz Editorial Team
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A pension fund is required to disburse a lump sum of $10,000,000 to its participants in 15 years. Assuming the fund earns an annual interest rate of 5%, compounded semi-annually, the present value needed today to fulfill this future obligation is closest to:
A
$4,767,427.
B
$4,810,171.
C
$4,892,771.
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