Everything Maths Grade 11

CHAPTER 6. FINANCE 6.8

For a quarterly interest rate of say 3% per quarter, the interest will be paid four timesper year (every
three months). We can calculate the effective annual interest rate by solving for i:

P(1 + i) = P(1 + i 4 )^4

where i 4 is the quarterly interest rate.

So (1 + i) = (1,03)^4 , and so i = 12,55%. This is the effective annual interest rate.

In general, for interest paid at a frequency of T times per annum, the follow equation holds:

P(1 + i) = P(1 + iT)T (6.7)

where iTis the interest rate paid T times per annum.

Decoding the Terminology EMBAB

Market convention however, is not to state the interest rate as say 1% per month, but rather toexpress
this amount as an annual amount which in this example would be paid monthly. This annual amount
is called the nominal amount.

The market conventionis to quote a nominal interest rate of “12% per annum paid monthly” instead
of saying (an effective) 1% per month. We knowfrom a previous example, that a nominal interest
rate of 12% per annum paid monthly, equates to an effective annual interest rate of 12 ,68%, and the
difference is due to theeffects of interest-on-interest.

So if you are given an interest rate expressed asan annual rate but paidmore frequently than annual,
we first need to calculate the actual interest paidper period in order to calculate the effective annual
interest rate.

monthly interest rate =

Nominal interest Rate per annum

number of periods per year

(6.8)

For example, the monthly interest rate on 12% interest per annum paidmonthly, is:

monthly interest rate =

Nominal interest Rate per annum

number of periods per year

=

12%

12 months

= 1% per month

The same principle applies to other frequenciesof payment.

Example 6: Nominal Interest Rate

QUESTION

Consider a savings account which pays a nominal interest at 8% per annum, paid quarterly.

Calculate (a) the interestamount that is paid eachquarter, and (b) the effective annual interest

rate.