If a credit card company charges 2% per month, how much would a person have to pay in interest for an amount of $1000 pending for a year at the end of the year.
The rate of interest is 2% per month. For 12 months the equivalent rate of interest is (1+.02) ^12 -1
This is approximately 26.82 %. The equivalent annual interest rate for the credit card is 26.82%. So for an amount of $1000, the interest to be paid is $268.2
This is the reason why the interest paid on the usage of credit cards is so high. People do not realize how much they are paying in interest as they usually see the monthly rate of interest and do not find it too high.
The basic approach in the answer #1 above is correct. However, the rate of interest assumed in the equation used is in terms of per unit rather than percentage.
Also please that the interest is compounded every month in line with general practice adopted by credit card companies.
r = percentage rate of interest per month = 2
n = number of months = 12 (given)
p = Principal amount of loan = $1000
The total amount of principle plus interest payable after n months is given by:
Total amount = p*(1 + r/100)^n
Substituting the given values in the above equation:
Total amount = 1000*(1 + 2/100)^12
Interest paid = (Total amount) - Principal
= 1268.24 - 1000
Interest = $268.24
Every month an interest of 2% per month for an amount of $1000 works out as follows.
At the end of the first month the the amount along with interest is 1000+1000*2% = 1000(1.02) = 1020 which is $1000+ interest $20
At the end of the 2nd month he has to pay 1020(1.02) = 1000(1.02)^2 = $1040*4 .= $1000 + interest $ 40.4.
Similarly at the end of the 12 th month $1000 becomes along with interest 1000(1.02)^12 = $1268.24 = $1000+ Interest $268.24.
So the interest to be at the end of the year = $268.24.
So he has to pay $268.24.
If it is simple interest then it would be 2%*12 = 24 % .
Simple interest = 1000*24% = $.240 which is less than compound interest by ($(268.240240) = $26.24