Most interest rates are quoted as an annual figure, which is fine if only one annual coupon or interest payment is payable. However a number of instruments require more frequent payment – for example, commercial mortgage payments. In order to be able to compare interest payments on a ‘like-for-like’ basis, we need to be able to recognise the impact of more frequent interest payments on the cost of the loan.
To calculate the effective annual rate:
\( Effective \: annual \: rate = 1 \:+ \:\frac{i}{n}n \:- \: 1\)
- Where: i = the nominal rate of interest
- And: n = the number of interest payments a year.
To give a worked example, consider a loan with a nominal interest rate of 8% with monthly interest payments.
\(The \: effective \: rate = 1 \: + \: \frac{i}{n}\:n \: – \: 1 = 1 \: + \: \frac{0.08}{12 } 12 \: – \: 1 \: * 100 = 8.299\%\)
Conventional calculator
When using a conventional calculator, to perform the calculation above you would need to press the following buttons:
0.08 ÷ 12 = (this will give the result 0.006666)
+ 1 = (this will give the result 1.006666)
M + (this will save the last result in the memory)
C (this will clear the display, but not the memory)
MR * MR * MR * MR * MR * MR * MR * MR * MR * MR * MR * MR = (this will give the result 1.08299)
– 1 = * 100 = (this will give the result 8.299)
Scientific calculator
Using the scientific calculator on a Windows computer (Start, Programs, Accessories, Calculator, View, Scientific), you would need to press the following buttons:
\(1 \: + \: \frac{ 0.08}{12} x \: ^\wedge \: y \: 12 =\: -1 = \:*100\: (this\: will\: give\: the\: result \:8.299)\)
HP12C
Using an HP12C:
.08 ENTER
12 ÷ 1 +
ENTER 12 yx
1 – 100 x (this will give the result 8.299)
