## Methodology Compound Interest Calculation (Updated October 2022)

A formula that can be used for calculating compound interest

```A = P( 1 + (r/n) )^nt ; R = r * 100

Where:
A= Total Accrued Amount (Principal + Interest)
P = Principal Amount
R = Rate of Interest per year as a decimal
; r = R/100 so 4% is 4 and r would be 0.04
t = number of periods
n = compounding period
(^ indicates to the power of)```

Reasoning – this breaks interest down into individual compounding periods. For example within a year, for months, r would be divided by 12 if the source of interest is annual based. The individual periods are then compounded using the power over all the periods eg 24 periods for 2 years – see the examples below. NOTE the r/n is an empirical adjustment required because quoted interest rates from most sources are over a year (annual). Whenever obtaining interest rates from a source we must be careful with the r/n calculation as it may need to be ignored. If for some reason the period over which interest is defined in the source list is anything other than annually this r/n calculation may need altered..

UK Base Interest Rates source
Bank of England Base Rate

XLS File of Base Rate changes since 1664 to June 2022
Note – I took a snap shot at June 2022 for latest go to bank of england base rate where there is(at October 2022) a constantly updated xls file.

So for example if we want to calculate interest on £100,000 over a period of 4 years and 8 months based on an interest rate of 4.0% over the base of 0.5% over differing compound periods;
Compounded annually;
A = 100,000 ( 1 + (0.045/1) )^4.67 = £122,821.10
A = £122,821.10

Compounded Monthly;
A = 100,000 ( 1 + (0.045/12) )^56 = £123,319.40
A = £123,319.40

Compounded Daily
A = 100,000 ( 1 + (0.045/365) )^1704 = 123,376.30
A = £123,376.30
Please note : simplification this calculation leap years re-calculate if important
(^ indicates to the power of)