## Simple and compound interest

##### Published: Feb 2006

Any investment which accrues interest is composed of two parts:

##### Principal

– the original investment.

##### Interest

– the interest which accrues on the original investment. How often the interest accrues, and how and when the interest is paid, will vary according to the exact terms of the investment.

There are two types of interest:

1. Simple interest is simply the amount paid to the investor for the investment, usually expressed as a percentage of the amount invested. This takes account of the interest that is earned on the principal investment only. It ignores the value of any interest paid during the term of the investment.
2. Compound interest includes the value of interest paid during the term of the investment. It takes account of interest that can be earned on any interest which is paid during the investment period. Therefore the total amount on which interest is calculated and paid increases over time. This process – known as compounding – is important when comparing interest rates which are applied frequently (say monthly) with a rate that is applied less frequently (say annually).

### Calculation of interest

To illustrate the difference between simple and compound interest we will consider an investment of RMB 1,000,000 over a year at an interest rate of 3% per annum.

To calculate simple interest, use the formula:

$$R\:=\:P \:1\:+\:r$$

$$where$$

• $$R\:=\: total \:return$$
• $$P\:= \:principal$$
• $$r\:= \:annual \:interest \:rate$$

So the total return would be:

$$1,000,000\:\times\:1\:+\:3\%\:=\:1,000,000\:\times\:1.03\:=\:1,030,000$$

This compound interest calculation would produce the same result if all the interest was paid at the end of the year. However, if the interest was paid monthly and added to the investment during the year, the total return should be calculated using the formula:

$$R\:=\:P \:1\:+\:\frac{r}{n}n$$

where

• $$R\:= \:total\: return$$
• $$P\:=\: principal$$
• $$r\:= \:annual\: interest\: rate$$
• $$n\:=\: number\: of\: interest \:payments\: during \:the\: year$$

If interest was paid monthly the total return would be:

$$1,000,000\:\times\:1\:+\:\frac{0.03}{12}12\:=RMB\: 1,030,416$$

So the compound interest would be RMB 30,416.

While these differences are small as a proportion of the whole sum, they will become much more significant for larger investments and longer periods. It is therefore vital to understand how interest is calculated and paid when comparing interest rates. This also applies to all forms of borrowing.

#### Calculation of compound interest

In the case of compound interest, the above calculation cannot be performed on a standard calculator as it contains an index higher than 1.

##### Scientific calculator

To perform the calculation using a Windows calculator in scientific setting, enter the following:

$$1,000,000\:*\:1\:+\:0.03\:/\:12\: x^y \:12\:=$$

This will give the result 1,030,416.

##### HP12C

Using an HP12C (or other calculator based on Reverse Polish Notation):

$$0.03\:ENTER\:12\:÷\:1\:+\: ENTER\: 12\: y^x\: 1,000,000\:\times$$

This will give the result 1,030,416.