FM Interest Rate Theory Flashcards

What is the relationship between the nominal rate compounded monthly (i^(12)) and the equivalent effective annual rate i?

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.

The force of interest δ is related to the effective annual rate i by which formula?

Answer: δ = ln(1 + i)

The force of interest δ equals the natural logarithm of the accumulation factor: δ = ln(1 + i).

An account pays a nominal interest rate of 6% compounded semiannually. What is the effective annual rate?

Answer: 6.09%

EAR = (1 + 0.06/2)^2 − 1 = (1.03)^2 − 1 = 0.0609 = 6.09%.

Under simple interest, the accumulation function a(t) is:

Answer: a(t) = 1 + it

Simple interest grows linearly, so the accumulation function is a(t) = 1 + it.

The discount rate d and the interest rate i satisfy which relationship?

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.

If the force of interest is δ = 0.05, what is the accumulation factor over 3 years under continuous compounding?

Answer: e^(0.15)

Under continuous compounding the accumulation factor is e^(δt) = e^(0.05 × 3) = e^(0.15).