Compounding frequency

To be precise, when stating an interest rate you need to define the time period for when interest is capitalised or compounded. This vital second ingredient is called by various different names. Sometimes we simply refer to the total number of periods but we need to know the compounding time interval – monthly, quarterly, yearly and so on. Technically we are referring to the compounding frequency, sometimes called accrual rate, or more often, the number of rests per annum.

For example, instead of paying 12% per annum, let’s see what happens to our typical £1,000 principal if interest is compounded at 1% per month – a twelfth of 12%. The table in Figure 3 shows that after 1 year (12 monthly periods) the end result, or future capital, is £1,126.83 as opposed to just £1,120 with the annual rests used in Figure 2.

Figure 3
Compounding monthly instead of annually
£1,000 invested (or borrowed) @ 1% per month interest, compounding monthly with no repayments.

	Interest	Capital	Notes
Principal		£1,000.00	Starting capital
End of month 1	£10.00	£1,010.00	Add 1% of £1,000
End of month 2	£10.10	£1,020.10	Add 1% of £1,010.00
End of month 3	£10.20	£1,030.30	Add 1% of £1,020.10
End of month 4	£10.30	£1,040.60	Add 1% of £1,030.30
End of month 5	£10.41	£1,051.01	Add 1% of £1,040.60
End of month 6	£10.51	£1,061.52	Add 1% of £1,051.01
End of month 7	£10.62	£1,072.14	Add 1% of £1,061.52
End of month 8	£10.72	£1,082.86	Add 1% of £1,072.14
End of month 9	£10.83	£1,093.69	Add 1% of £1,082.86
End of month 10	£10.94	£1,104.62	Add 1% of £1,093.69
End of month 11	£11.05	£1,115.67	Add 1% of £1,104.67
End of Month 12	£11.16	£1,126.83	Add 1% of £1,115.67

After 12 months the principal has increased by £126.83, which is 12.683% in one year. With annual compounding it would have increased by only £120 or 12%.