- 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.