# If a loan for $10,000 is paid off in 5 years and the rate of interest is n% per annum componded monthly, how much is paid as interest over the course of the loan?

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### 2 Answers

The reference gives loan repayment calculators for both simple and compound interest. In the situation of compound interest, the interest amount for the first month is added to the principal on which interest is due for the second month, and so on.

For the simple interest calculator, insert 10,000.00 as the loan amount, 60 months for the time period, and 10% for the interest rate.

For the compound interest calculator, insert the same figures.

Results are as follows:

Simple Interest = $2,748.20

Compound Interest = $6,105.10

Note: The amount you calculate will not necessarily match the amount calculated by the bank. This is because the bank usually posts added fees such as administration fees.

If the rate of interest is r%, per annum and the period of loan duration is 5years and the interest compounds every month,then:

The monthly interest = r%/12 = r/1200.

Compounding monthly means the interest acrued for the month is added to the principal at the beginning of the month and the resulting total amount is treated as princpal for next month and acrues the interest during the next month. The process continues till the the end of 60 months.

So,the amount of 10000 along with interest at the end of 1st month becomes 10000+10000*r/1200 = 10000(1+r/1200)

At the end of 2nd month the amount with interest = the amount at the end of first month alon with interest *(1+r/1200)=

=10000(1+r/1200)(1+r/1200)=10000(1+r/1200)^2 =

The amount at the end of 3rd month aalong with interest =

={10000(1+r/1200)^2 }*(1+r/1200) =10000(1+r/1200)^3.

By the above compounding process at the end of 5 years or 60 months amount along with compound interest becomes 10000(1+r/1200)^60

The cost of the interest for 5 years compounded on monthly basis over 10000 = Total amount along with interest minus the loan of 10000

=10000(1+r/1200)^60 - 10000

={10000(1+r/1200)^60 -1}.

=512.49 for r=1%

=1050.79 for r=2%

=1616.16 for r=3%

=2209.97 for r=4%

=2833.59 for r=5%

=3488.50 for r= 6%

=4176.25 for r=7%

=4898.46 for r=9%

=6453.08 for r=10%

Had he taken the loan at simple interest, then for 10000, the interest for 5 years would have been Pnr/100 =10000*5*r/100 =500r = 500 for r=1%, 1000 for =2%, 1500 for r=3%, 2000 for r=4%, 2500 for r=5%, 3000 for r=6%, 3500 for r=7%, 4000 for r=8%, 4500 for r=9% and 5000 for r=10%.