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Answer: 3.98%.
The investor will be indifferent between the two term deposits if their effective annual rates (EAR) are identical. For Term Deposit 1, the EAR is calculated as follows: \[ \text{EAR} = \left(1 + \frac{0.04}{4}\right)^4 - 1 = 0.040604 \] For Term Deposit 2, the stated annual rate with continuous compounding must equate to this EAR. Therefore: \[ 0.040604 = e^r - 1 \] Solving for \( r \): \[ r = \ln(1.040604) \approx 0.039801 \text{ or } 3.98\% \] Option B is correct because it accurately reflects the required stated annual rate for Term Deposit 2. Option A is incorrect as it uses the natural logarithm of the stated annual rate instead of the EAR. Option C is incorrect as it represents the EAR of Term Deposit 1, not the stated annual rate for Term Deposit 2.
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An investor is evaluating two term deposits with the following attributes: Term Deposit 1: Quarterly compounding, Stated annual rate of 4%. Term Deposit 2: Continuous compounding, Stated annual rate to be determined. To ensure the investor is indifferent between the two term deposits, the stated annual rate for Term Deposit 2 should be closest to:
A
3.92%.
B
3.98%.
C
4.06%.