2005/08/31

The secret of loan

Recent, I was interested in the calculation of mortgage loan and car loan. Basically, the bank will give you an annual percent rate for the loan amount and years of the loan. And with a calculation program, they will figure out the monthly payment. But, here, the bankers make a tiny assumption, which is flaw for the rigorous arithmatic, but is ok for our common sense. This tiny assumption is that the monthly rate is one twelveth of annual rate:A=12M, rather than the calculated by the complicated formula: 1+A=(1+M)^12. This tiny difference makes $7,000 difference for a 30 year loan of $300,000 with 5% apr, which is about 1% of total payment. But, anyway, we have no choice, since every banker do the samething.

So, the final monthly payment for a loan, without regarding tax and other fees, is MonthlyPayment=LoanAmount*APR/(1-1/(1+APR)^YearsOfLoan)/12:

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