The compound interest scheme is the most common in the financial system and is therefore the most useful for calculating day to day problems. Interest generated for each period is incorporated into the principal for the calculation of interest for the following period.
We call capitalization the moment interest is incorporated into the principal.
After three months of capitalization, we have:
1st month: M = P. (1 + i)
2nd month: principal equals previous month amount: M = P. (1 + i). (1 + i)
3rd month: principal equals previous month amount: M = P. (1 + i). (1 + i). (1 + i)
Simply put, we get the formula:
M = P. (1 + i)^{no} |
Important: the rate i has to be expressed to the same extent as no, ie interest rate per month for n months.
To calculate interest only, decrease the principal amount at the end of the period:
J = M - P |
Example:
Calculate the amount of a capital of $ 6,000, applied to compound interest, for 1 year at the rate of 3.5% per month. (use log 1.035 = 0.0149 and log 1.509 = 0.1788)
Resolution:
P = $ 6,000.00
t = 1 year = 12 months
i = 3.5% a.m. = 0.035
M =?
Using the formula M = P. (1 + i)^{no}, we get:
M = 6000. (1 + 0.035)^{12} = 6000. (1,035)^{12} = 9066,41
Therefore the amount is $ 9,066.41.
Next: Relationship between Interest and Progressions