The nominal risk-free rate represents the return on a risk-free investment that includes compensation for expected inflation. It is approximated by adding the real risk-free rate (which reflects the time value of money in the absence of inflation) and an inflation premium to account for the anticipated erosion of purchasing power.

To calculate future value using continuous compounding, use the formula:

FV = PV \times e^{rt}

Where:

• PV=3,500

• r=0.055

• t=6

• e^{0.055\times6}=e^{0.33} = 1.3901

FV = 3,500 x 1.3901 = 4,865.35

Steps on BA II Plus Calculator:

1. Calculate exponent:
   0.055 × 6 = 0.33

2. Press 2nd → LN (to access e^x)
   → displays e^0.33 ≈ 1.3901

3. Multiply:
   1.3901 × 3500 = 4,865.35

Final Answer: $4,865

The key factor contributing to the yield difference between bonds issued by a developed country's government and an emerging market corporation is credit risk. Investors demand a higher yield from the corporate issuer in an emerging market to compensate for the higher probability of default or financial instability. Inflation and reinvestment risks are generally comparable for bonds of the same maturity unless otherwise noted, making credit risk the primary differentiator in this case.

To find the present value (PV) with monthly compounding, use the formula:
PV = FV × (1 + r/m)^−mN

Where:

• FV = 6,000

• r = 6% or 0.06 (annual interest rate)

• m = 12 (monthly compounding periods)

• N = 4 (years)

Step-by-step calculation:
PV = 6,000 × (1 + 0.06/12)^−12×4
 = 6,000 × (1.005)^−48
 = 6,000 × 0.787098
 ≈ $4,722.59

Using a BA II Plus calculator:

• FV = 6,000

• I/Y = 0.5 = (6% ÷ 12)

• N = 48

• PMT = 0

• CPT → PV

• Result: PV ≈ $4,722.59

A is correct. The continuously compounded rate of return is calculated using the formula:

r = In(S_{T}\div S_{0})

S_{T} = The price of the stock after one year.

S_{0} = The price of the stock at time 0.

How to solve using the BAII plus

• 1,050 / 980 = 1.07142857

• Press LN

• The result should be 0.06899287 or 6.99%

R_{g} = [(1 + 0.120) × (1 − 0.040) × (1 + 0.085) × (1 + 0.182) × (1 + 0.056)^{1/5} − 1]

The maturity premium compensates investors for the additional risk they bear due to longer holding periods. As maturity increases, the bond’s market value becomes more sensitive to interest rate fluctuations.

• Choice A describes the liquidity premium.

• Choice B describes the default risk premium.

A is correct. The harmonic mean is appropriate for calculating the average purchase price per unit when equal amounts are invested each year. It gives equal weight to each unit purchased and adjusts for price variation.

x_{h} = 4 ÷ [(1/50.00) + (1/66.00) + (1/72.00) + (1/82.00)]

B is correct. The geometric mean reflects the compound rate of return over multiple periods and is the appropriate measure for evaluating investment performance over time.

• A is close, but the key concept is that the geometric mean is always less than or equal to the arithmetic mean when returns vary — not that the arithmetic mean always "exceeds" it.

• C is incorrect because the arithmetic mean does not account for compounding and may overstate long-term performance.

A is correct. The required return is the minimum acceptable return on an investment, reflecting its risk. If an investment does not meet this threshold, it should be rejected.

• B is incorrect because an opportunity cost refers to the value of the next best alternative forgone, not the minimum return.

• C is incorrect because a sunk cost is an expense that has already occurred and cannot be recovered or changed.