Chartered Financial Analyst Level 1

Get started today

Ultimate access to all questions.

Explanation:

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.

Explanation:

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.

Comments (0)

No comments yet.

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:

Exam-Like

$4,767,427.

100.0%

$4,810,171.

0.0%

$4,892,771.

Chartered Financial Analyst Level 1

Get started today

Comments (0)

Get started today

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:

Comments (0)

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: