Workshop W2: Interest Rates (FINM1001)

What are the 3 types of Interest Rates?

1. Annual effective interest rate (r_e).

2. Annual nominal interest rate (r_n).

3. Periodic interest rate (r_p).

Annual effective interest rate (r_e)

Where the frequency of charging/payment matches the period specified by the interest rate (i.e., the rate is quoted annually and is applied annually).

E.g., 12% p.a. compounded annually.

Annual nominal interest rate (r_n)

Where interest is charged more frequently than the time period specified in the interest rate.

E.g., 12% p.a. compounded monthly.

Periodic interest rate (r_p)

The rate of interest applied per compound period in the case of a nominal interest rate.

E.g., if the nominal interest rate is 12% compounded semi-annually:

• The periodic interest rate is 12%/2 = 6% per six-months.

When do you use an Annual Effective Rate?

To calculate future or present value when:

• You have an annuity / perpetuity with annual cash flows. Here, you must also have n expressed in terms of number of years; or,

• You have multiple uneven cash flows / a single cash flow and you want to express n in terms of the number of years.

When do you use a Periodic Interest Rate?

When:

• You have an annuity / perpetuity with cash flows paid less than annually. Here, the periodic rate must be expressed as frequently as the cash flows.

• You have multiple uneven cash flows / a single cash flow and you want to use a value of n calculated based on the same period as the period rate.

When do you use an Annual Nominal Rate?

Never.

What interest rate do you use if you have a single cash flow / multiple uneven cash flows?

You can choose whether to use an annual effective or a periodic rate, and you must use a value of n calculated based on the same period as the interest rate.

E.g., if you have a single cash flow in 5 years time:

• If you use a monthly interest rate: n = 5×12 = 60.

• If you use an annual effective interest rate: n = 5.

What interest rate do you use if you have a an annuity / perpetuity?

You must use an interest rate of the same frequency of the cash flows, and you must use a value of n calculated based on the same period (in the case of annuities).

Examples:

• If you have monthly cash flows for 5 years, you must use a monthly interest rate and n = 5×12 = 60.

• If you have yearly cash flows for 5 years, you must use an annual effective interest rate and n = 5.

• If you have quarterly cash flows forever, you must use a quarterly interest rate.

The Interest Rate Wheel

Interest Rate Quick Check: r_n to r_p

1. How frequently do cash flows occur?

2. How frequently is the annual nominal rate compounded?

3. If answers 1 and 2 match: r_n → r_p.

4. If answers 1 and 2 do not match:

   a) Convert r_n → r_e.

   b) Convert r_e → r_p.