Chapter 5: Interest Rates

Question 1

What is a nominal interest rate?

Answer 1

A nominal interest rate is the annual interest rate without considering compounding. It’s just the rate divided by the number of periods in a year.

Question 2

What is the formula for nominal interest rate per period?

Answer 2

i(p)/p

Question 3

How do you convert from an effective interest rate to a nominal interest rate?

Answer 3

To convert from effective to nominal interest:
i(p) = P × [(1 + i)^(1/P) - 1]
Where:
i = effective interest rate
P = number of compounding periods in a year
i(p) = nominal interest rate

Question 4

How do you convert from a nominal interest rate to an effective interest rate?

Answer 4

To convert from effective to nominal interest:
1+i = (1 + i(p) /p)^(P)
Where:
i = effective interest rate
P = number of compounding periods in a year
i(p) = nominal interest rate

Question 5

What is a nominal discount rate?

Answer 5

A nominal discount rate is the annual discount rate stated without adjusting for compounding periods. It is used to calculate the present value of future cash flows, but doesn’t account for how often interest is compounded.

Question 6

What is the force of interest?

Answer 6

The force of interest is a continuous compounding interest rate, denoted by δ (delta). It measures how interest accumulates continuously over time, rather than at discrete intervals.

Question 7

What is the formula for the effective interest rate 𝑖 in terms of the force of interest 𝛿?

Answer 7

i=e^δ −1

Question 8

What is the formula for the discount factor
𝑣 in terms of the force of interest 𝛿?

Answer 8

v=e ^ −δ

Question 9

What is the formula for the discount rate
𝑑 in terms of the force of interest δ?

Answer 9

d=1−e ^−δ

Question 10

What is the formula for the force of interest
𝛿 in terms of the effective interest rate 𝑖?

Answer 10

δ=ln(1+i)

Question 11

What is the formula for the force of interest
𝛿 in terms of the discount factor 𝑣?

Answer 11

δ=−ln(v)

Question 12

What is the formula for the force of interest
𝛿 in terms of the discount rate 𝑑?

Answer 12

δ=−ln(1−d)

Question 13

What is the formula for the effective interest rate 𝑖 in terms of the discount rate 𝑑?

Answer 13

i= (1−d)^-1 -1=1/(1−d) -1
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Question 14

What is the formula for the effective interest rate 𝑖 in terms of the discount factor 𝑣?

Answer 14

i= v^-1 −1

Question 15

What is the formula for the discount factor
𝑣 in terms of the effective interest rate 𝑖?

Answer 15

v= (1+i)^-1

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Question 16

What is the formula for the discount factor 𝑣 in terms of the discount rate 𝑑?

Answer 16

v=1−d

Question 17

What is the formula for the discount rate 𝑑
in terms of the effective interest rate 𝑖?

Answer 17

d= i/1+i​

Question 18

What is the formula for the discount rate
𝑑 in terms of the discount factor 𝑣?

Answer 18

d=1−v