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- WELCOME TO A LESSON ON THE LOAN PAYMENT FORMULA. THE GOAL OF THE VIDEO IS TO DETERMINE THE PAYMENT FOR A FIXED INSTALLMENT LOAN. INSTALLMENT BUYING IS WHEN YOU PURCHASE SOMETHING TODAY WITH A LOAN THAT YOU PAY BACK WITH EQUAL PAYMENTS OVER A PERIOD OF TIME, USUALLY MONTHLY FOR A PERIOD OF YEARS. THE TWO MOST COMMON EXAMPLES WOULD BE FOR A CAR LOAN OR A HOME MORTGAGE LOAN, AND WELL TAKE A LOOK AT AN EXAMPLE OF BOTH OF THESE. HERE IS THE LOAN PAYMENT FORMULA FOR FIXED AMOUNT OF EQUAL PAYMENTS WHERE R IS THE ANNUAL NOMINAL INTEREST RATE EXPRESSED AS A DECIMAL, T IS THE TIME IN YEARS, N IS THE NUMBER OF COMPOUNDS PER YEAR. P IS THE AMOUNT OF THE LOAN, AND PMT REPRESENTS THE MONTHLY PAYMENT. LETS TAKE A LOOK AT WHERE THIS FORMULA COMES FROM. IT COMES FROM THE COMPOUNDED INTEREST FORMULA AND THE VALUE OF ANNUITY FORMULA. SO IF YOURE THE BANK OR THE LENDER YOU WOULD USE THE COMPOUNDED INTEREST FORMULA TO DETERMINE THE RETURN ON YOUR INVESTMENT. AND IF YOU WERE THE PERSON