– WELCOME TO AN EXAMPLE OF DETERMINING THE MONTHLY LOAN
PAYMENT FOR A MORTGAGE. THE PRICE OF A HOME IS \$155,000. THE REQUIRED DOWN PAYMENT IS 10% AND YOU QUALIFY FOR A 30 YEAR
FIXED MORTGAGE AT 5.5%. NUMBER ONE, WE WANT TO DETERMINE
THE DOWN PAYMENT AND THE LOAN AMOUNT. NUMBER TWO, WE WANT TO FIND
THE MONTHLY MORTGAGE PAYMENT, AND, NUMBER THREE, DETERMINE
HOW MUCH INTEREST IS PAID OVER THE LIFE OF THE LOAN. SO FOR NUMBER ONE, SINCE THE
DOWN PAYMENT REQUIREMENT IS 10%, WE WANT TO FIND 10% OF 155,000. SO THAT WOULD BE 155,000 x 10%
EXPRESSED AS A DECIMAL, WHICH WOULD BE 0.10
OR, IF WE WANT, JUST 0.1. THIS WOULD BE \$15,500. OF COURSE, IF WE WANT TO CHECK
THIS WE CAN USE A CALCULATOR, 155,000 x 0.1 OR 0.10=\$15,500. SO IF THIS IS THE DOWN PAYMENT
THEN THE LOAN AMOUNT IS EQUAL TO THE PRICE OF THE
HOME 155,000 – THE DOWN PAYMENT, SO THIS WOULD GIVE US \$139,500. THIS WOULD BE THE LOAN AMOUNT. AND NOW FOR NUMBER TWO WE WANT TO FIND THE MONTHLY
MORTGAGE PAYMENT. TO DO THIS BY HAND WE’LL BE
USING THIS FORMULA HERE. I’LL ALSO SHOW HOW TO USE
THE TI84 GRAPHING CALCULATOR TO DETERMINE
THE MONTHLY PAYMENT. SO FIRST USING OUR FORMULA, THE MONTHLY PAYMENT IS GOING TO
BE EQUAL TO THIS QUOTIENT HERE WHERE P IS THE LOAN AMOUNT
OF 139,500 x R DIVIDED BY N WHERE R IS THE ANNUAL INTEREST
RATE AND N IS THE NUMBER OF PAYMENTS
PER YEAR. SO R IS 5.5%, EXPRESSED AS
A DECIMAL THAT WOULD BE 0.055. OR MAKING MONTHLY PAYMENTS, SINCE THERE’S 12 MONTHS
IN A YEAR N IS 12 DIVIDED BY 1 – THE
QUANTITY 1 + R DIVIDED BY N, WHICH, AGAIN, IS 0.055
DIVIDED BY 12 RAISED TO THE POWER OF -N x T,
WHICH IS -12 x T, WHICH IS TIME IN YEARS. THIS IS A 30 YEAR FIXED MORTGAGE
SO T IS 30. AND NOW WE’LL GO
TO THE CALCULATOR. LET’S EVALUATE THE NUMERATOR AND
DENOMINATOR SEPARATELY FIRST. SO FOR THE NUMERATOR WE’LL HAVE
139,500 x 0.055 DIVIDED BY 12. SO THE NUMERATOR IS 639.375. AND NOW FOR THE DENOMINATOR
WE’LL HAVE 1 – THE QUANTITY 1 + 0.055 DIVIDED BY 12 RAISED TO
THE POWER OF THIS WOULD BE -360, AND ENTER. SO WE HAVE APPROXIMATELY
0.80722. AND NOW WE’LL GO AHEAD
AND FIND THIS QUOTIENT.   SO THE MONTHLY PAYMENT IS GOING
TO BE APPROXIMATELY \$792.07. KEEP IN MIND, THIS DOES NOT
INCLUDE TAXES AND INSURANCE. LET’S ALSO VERIFY THIS USING THE FINANCE MENU
OF THE GRAPHING CALCULATOR. SO WE’RE GOING TO PRESS APPS,
ENTER FOR FINANCE, AND THEN ENTER FOR TMV SOLVER. N IS THE NUMBER OF PAYMENTS
IN THE LOAN THAT WOULD BE 30 x 12 OR 360. THE INTEREST RATE IS 5.5%. EV IS THE PRESENT VALUE
OF THE LOAN, WHICH IS THE LOAN AMOUNT
OF \$139,500. WE’LL COME BACK TO THE PAYMENT. THE FUTURE VALUE WOULD BE 0
AFTER THE LOAN IS PAID. PAYMENTS PER YEAR IS 12, NUMBER OF COMPOUNDS PER YEAR
IS ALSO 12. PAYMENTS ARE MADE
AT THE END OF THE MONTH. SO NOW WE’LL GO BACK UP TO PMT
FOR PAYMENT. WE’RE GOING TO CLEAR THIS AND NOW WE’RE GOING
TO PRESS ALPHA, ENTER FOR SOLVE. SO ALPHA, ENTER, VERIFIES THAT
OUR MONTHLY PAYMENT WOULD BE \$792.07 ROUNDED
TO THE NEAREST CENT. REMEMBER WE ALSO ROUNDED
OUR DENOMINATOR HERE. AND NOW FOR THE LAST QUESTION
WE’RE GOING TO DETERMINE HOW MUCH INTEREST IS PAID
OVER THE LIFE OF THE LOAN. LET’S FIRST DETERMINE THE AMOUNT
PAID OVER THE LIFE OF THE LOAN. THAT WOULD BE THE MONTHLY
PAYMENT, WHICH IS \$792.07 x THE NUMBER
OF MONTHS OVER 30 YEARS. SO THIS WOULD BE x 30 x 12. SO WE HAVE \$792.07 x 360,
OR IF WE WANT 30 x 12, SO OVER 30 YEARS A TOTAL
OF \$285,145.20 WILL BE PAID. WELL, REMEMBER THE LOAN AMOUNT,
OR THE AMOUNT BORROWED, WAS \$139,500. SO THE DIFFERENCE OF THESE
TWO AMOUNTS WOULD BE THE AMOUNT OF INTEREST
PAID. SO WE’LL GO AHEAD AND TAKE
THIS AMOUNT HERE AND SUBTRACT THE LOAN AMOUNT
\$139,500. SO \$145,645.20 IS THE AMOUNT OF
INTEREST PAID OVER THE 30 YEARS.   NOTICE THE AMOUNT OF INTEREST
PAID IS ACTUALLY MORE THAN
THE ORIGINAL LOAN AMOUNT. I HOPE YOU FOUND THIS EXAMPLE
HELPFUL. THE NEXT EXAMPLE WE’LL TAKE
A LOOK AT A LOAN THAT ALSO HAS POINTS.