FM FM Interest Rate Theory

Question 1

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

Accepted Answer

(1 + i) = (1 + i^(12)/12)^12

Answer

(1 + i) = (1 + i^(12))^12

Answer

(1 + i) = 12 × i^(12)

Answer

(1 + i) = (1 + 12 × i^(12))^(1/12)

Question 2

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

Accepted Answer

δ = ln(1 + i)

Answer

δ = i / (1 + i)

Answer

δ = e^i − 1

Answer

δ = 1 − e^(−i)

Question 3

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

Accepted Answer

6.09%

Answer

6.00%

Answer

6.14%

Answer

5.91%

Question 4

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

Accepted Answer

a(t) = 1 + it

Answer

a(t) = (1 + i)^t

Answer

a(t) = e^(δt)

Answer

a(t) = 1 + d·t / (1 − d·t)

Question 5

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

Accepted Answer

d = i / (1 + i)

Answer

d = i × (1 + i)

Answer

d = 1 − i

Answer

d = i − 1

Question 6

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

Accepted Answer

e^(0.15)

Answer

e^(0.05)

Answer

(1.05)^3

Answer

1 + 0.05 × 3