# Math

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John Receive a 10,000 loan, with an interest rate of 6 %, for 6 years.

What is the total amount of interest paid to the bank?

• Math -

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. 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.

Typically, loan, or mortgage payments, the interest compounding periods and loan payment periods are the same but can be different, depending on the rules of the lending institution. For instance, if the quoted loan interest rate is 8%, the interest is compounded quarterly, and the loan payments are monthly, one must convert the nominal annual rate to an annual effective rate which is then combined with the rate for the payment periods stated. For instance, given the 8%, compounded quarterly results in (1.02)^4 = 1.0824 annual effective rate, the monthly rate applied to the loan payment calculation is .0824/12 = .006866.

This should be suffic1ent for you to solve your specific problem.

• Math -

what is the apr if the amount Financed \$3500; Interest Charged \$ 675; Number of Payments 24

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