#### paradox6996

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- Thread starter paradox6996
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The formula for calculating a monthly loan payment is R = Pi/[1 - 1/(1+i)^n] where R = the periodic payment, P = the principal, or debt to be paid off, n = the number of payment periods over which the payments will take place, and i = the periodic interest rate in decimal form. The interest rate for a loan is usually quoted as an annual rate such as 8%. In the formula the first thing we do is convert this to i = .08 when considering annual payments.

If payments are to be made monthly, i = .08/12 = .006666 as the monthly interest rate. An example will illustrate the use of the formula.

Lets say you want to borrow $10,000 for a home improvement, to be paid off monthly over a period of 5 years, with an annual interest rate of 8%. So P = 10,000, n = 5 x 12 = 60, i = .08/12 = .006666. Then we have R = 10000(.006666)/[1 - 1/(1+.006666)^60] = 66.66/[1 - 1/(1.489790] = 66.66/.328764 = $202.76 per month. As simple as that. Over the life of the loan you will pay $12,165.49 back to the bank thereby incurring the cost of $2,165.49 for the priviledge of borrowing the money.

Are you sure there are such loans? They are evidently "single payment loans".paradox6996 said:I'm writing a program that calculates someones consumer loan. If we use $1000 as principle, and 15%(.15) as the rate and the duration of the loan is 18 months, you would in the end only get $775 because the the interest is deducted from the principle leaving you with 775$ from $1000.

Seems illegal: you're charged interest on 1000, but get only 775.

I presume 15% is used for calculation purposes, and is not the interest rate

declared on the contract; borrowing 775 and paying back 1000 18 months later

calls for a rate of ~17.11 % cpd. monthly.

Anyway, if you simply need the mechanics:

t = total loan (1000)

c = cash proceeds (775)

r = rate (.15)

n = number of months (18)

Formula: t = 12c / (12 - rn)

If the borrower wishes to obtain $775 (your example):

t = 12(775) / (12 - .15(18)) = 1000 = amount of loan to request

Another example:

you wish to get $1200, rate is 9%, time is 27 months:

t = 12(1200) / (12 - .09(27)) = ~1504.70 = amount to request