FM FM Interest Rate Theory 1 — Questions and Answers
Question 1: What is the relationship between the nominal rate compounded monthly (i^(12)) and the equivalent effective annual rate i?
- (1 + i) = (1 + i^(12)/12)^12 (Correct answer)
- (1 + i) = (1 + i^(12))^12
- (1 + i) = 12 × i^(12)
- (1 + i) = (1 + 12 × i^(12))^(1/12)
Correct answer: (1 + i) = (1 + i^(12)/12)^12
The effective annual rate i satisfies (1 + i) = (1 + i^(12)/12)^12, converting monthly compounding to an annual equivalent.
Question 2: The force of interest δ is related to the effective annual rate i by which formula?
- δ = ln(1 + i) (Correct answer)
- δ = i / (1 + i)
- δ = e^i − 1
- δ = 1 − e^(−i)
Correct answer: δ = ln(1 + i)
The force of interest δ equals the natural logarithm of the accumulation factor: δ = ln(1 + i).
Question 3: An account pays a nominal interest rate of 6% compounded semiannually. What is the effective annual rate?
- 6.09% (Correct answer)
- 6.00%
- 6.14%
- 5.91%
Correct answer: 6.09%
EAR = (1 + 0.06/2)^2 − 1 = (1.03)^2 − 1 = 0.0609 = 6.09%.
Question 4: Under simple interest, the accumulation function a(t) is:
- a(t) = 1 + it (Correct answer)
- a(t) = (1 + i)^t
- a(t) = e^(δt)
- a(t) = 1 + d·t / (1 − d·t)
Correct answer: a(t) = 1 + it
Simple interest grows linearly, so the accumulation function is a(t) = 1 + it.
Question 5: The discount rate d and the interest rate i satisfy which relationship?
- d = i / (1 + i) (Correct answer)
- d = i × (1 + i)
- d = 1 − i
- d = i − 1
Correct answer: d = i / (1 + i)
The discount rate d = i / (1 + i), reflecting that d is paid at the beginning of the period while i is paid at the end.
Question 6: If the force of interest is δ = 0.05, what is the accumulation factor over 3 years under continuous compounding?
- e^(0.15) (Correct answer)
- e^(0.05)
- (1.05)^3
- 1 + 0.05 × 3
Correct answer: e^(0.15)
Under continuous compounding the accumulation factor is e^(δt) = e^(0.05 × 3) = e^(0.15).
FM FM Interest Rate Theory 1
What is the relationship between the nominal rate compounded monthly (i^(12)) and the equivalent effective annual rate i?