Everything Maths Grade 11

6.8 CHAPTER 6. FINANCE

SOLUTION

Step 1 : Determine what is given and what is required

We are given that a savings account has a nominal interest rate of 8% paid

quarterly. We are required to find:

• the quarterly interest rate, i 4


• the effective annual interest rate, i

Step 2 : Determine how to approach the problem

We know that:

quarterly interest rate =

Nominal interest Rate per annum

number of quarters peryear

and

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

where T is 4 because there are 4payments each year.

Step 3 : Calculate the monthlyinterest rate

quarterly interest rate =

Nominal interest rate per annum

number of periods per year

=

8%

4 quarters

= 2% per quarter

Step 4 : Calculate the effectiveannual interest rate

The effective annual interest rate (i) is calculated as:

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

(1 + i) = (1 + 2%)^4

i = (1 + 2%)^4 − 1

= 8,24%

Step 5 : Write the final answer

The quarterly interest rate is 2% and the effective annual interest rate is 8 ,24%,

for a nominal interest rate of 8% paid quarterly.