We assume the nominal rate of the interest to be r percent per annum, the principal loan amount burrowed to be P .
Then the monthly interest works out (r/12)% = r/1200 per rupee or per dollar or per unit of money. Period of compounding is month.
The loan amount growing by compound interest: The loan amount of P grows in one month=P(1+r/1200) along with interest.
The loan amount P grows to P(1+r/1200)^ 2 in 2 months, along with interest.
The loan amount grows to become P(1+r/1200)^12 in 12 months or one year period together with interest.
The loan amount with interest,therefore, grows to become P(1+r/1200)^60 in 60 months or 5 years, period. Take off the principal loan amount from the grown amount with interest in 5 years, and then you get what costed you the compound interest over your loan of P .
Therefore , the cost of compound interest for the Principal loan amount ,P for 5 years, compounding being monthly = the amount loan grown in 5 years minus principal amount of loan=
=P(1+r/1200)^60 -P= P{(1+r/1200)^60 - 1}
Therefore, the cost of compound interest for 5 years on 1 unit of money = P(1+r/1200)^60 -1}/P = (1+r/1200)^60 -1. From this we can construct a table for different rates of interest for different principal loan amount and get the cost of compound interest for 5 years ,compounding monthly, as below:
Loan Vs Interest rate : cost of compound interest for 5 years at rates:
Amoun(principal)Loan : 1% 2% 3% 4% 5%
1 0.0512 0.1051 0.1616 0.2210 0.2834
100 5.12 10.50 16.16 22.10 28.34
10000 512.49 1050.08 1616.16 2209.97 2833.59
The construction of the table can be extended simimarly for different rate of nominal interests, and for different principles and we can use it to get any intermediate values , by interpolation if requred.
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