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Ex 1: Find a Monthly Mortgage Payment with a Down Payment - YouTube
Channel: Mathispower4u
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- WELCOME TO AN EXAMPLE
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OF DETERMINING THE MONTHLY LOAN
PAYMENT FOR A MORTGAGE.
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THE PRICE OF A HOME IS $155,000.
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THE REQUIRED DOWN PAYMENT IS 10%
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AND YOU QUALIFY FOR A 30 YEAR
FIXED MORTGAGE AT 5.5%.
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NUMBER ONE, WE WANT TO DETERMINE
THE DOWN PAYMENT
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AND THE LOAN AMOUNT.
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NUMBER TWO, WE WANT TO FIND
THE MONTHLY MORTGAGE PAYMENT,
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AND, NUMBER THREE, DETERMINE
HOW MUCH INTEREST IS PAID
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OVER THE LIFE OF THE LOAN.
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SO FOR NUMBER ONE, SINCE THE
DOWN PAYMENT REQUIREMENT IS 10%,
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WE WANT TO FIND 10% OF 155,000.
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SO THAT WOULD BE 155,000 x 10%
EXPRESSED AS A DECIMAL,
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WHICH WOULD BE 0.10
OR, IF WE WANT, JUST 0.1.
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THIS WOULD BE $15,500.
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OF COURSE, IF WE WANT TO CHECK
THIS WE CAN USE A CALCULATOR,
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155,000 x 0.1 OR 0.10 = $15,500.
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SO IF THIS IS THE DOWN PAYMENT
THEN THE LOAN AMOUNT
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IS EQUAL TO THE PRICE OF THE
HOME 155,000 - THE DOWN PAYMENT,
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SO THIS WOULD GIVE US $139,500.
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THIS WOULD BE THE LOAN AMOUNT.
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AND NOW FOR NUMBER TWO
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WE WANT TO FIND THE MONTHLY
MORTGAGE PAYMENT.
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TO DO THIS BY HAND WE'LL BE
USING THIS FORMULA HERE.
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I'LL ALSO SHOW HOW TO USE
THE TI84 GRAPHING CALCULATOR
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TO DETERMINE
THE MONTHLY PAYMENT.
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SO FIRST USING OUR FORMULA,
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THE MONTHLY PAYMENT IS GOING TO
BE EQUAL TO THIS QUOTIENT HERE
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WHERE P IS THE LOAN AMOUNT
OF 139,500 x R DIVIDED BY N
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WHERE R IS THE ANNUAL INTEREST
RATE
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AND N IS THE NUMBER OF PAYMENTS
PER YEAR.
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SO R IS 5.5%, EXPRESSED AS
A DECIMAL THAT WOULD BE 0.055.
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OR MAKING MONTHLY PAYMENTS,
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SINCE THERE'S 12 MONTHS
IN A YEAR
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N IS 12 DIVIDED BY 1 - THE
QUANTITY 1 + R DIVIDED BY N,
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WHICH, AGAIN, IS 0.055
DIVIDED BY 12
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RAISED TO THE POWER OF -N x T,
WHICH IS -12 x T,
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WHICH IS TIME IN YEARS.
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THIS IS A 30 YEAR FIXED MORTGAGE
SO T IS 30.
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AND NOW WE'LL GO
TO THE CALCULATOR.
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LET'S EVALUATE THE NUMERATOR AND
DENOMINATOR SEPARATELY FIRST.
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SO FOR THE NUMERATOR WE'LL HAVE
139,500 x 0.055 DIVIDED BY 12.
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SO THE NUMERATOR IS 639.375.
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AND NOW FOR THE DENOMINATOR
WE'LL HAVE 1 - THE QUANTITY 1
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+ 0.055 DIVIDED BY 12 RAISED TO
THE POWER OF THIS WOULD BE -360,
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AND ENTER.
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SO WE HAVE APPROXIMATELY
0.80722.
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AND NOW WE'LL GO AHEAD
AND FIND THIS QUOTIENT.
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SO THE MONTHLY PAYMENT IS GOING
TO BE APPROXIMATELY $792.07.
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KEEP IN MIND, THIS DOES NOT
INCLUDE TAXES AND INSURANCE.
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LET'S ALSO VERIFY THIS
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USING THE FINANCE MENU
OF THE GRAPHING CALCULATOR.
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SO WE'RE GOING TO PRESS APPS,
ENTER FOR FINANCE,
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AND THEN ENTER FOR TMV SOLVER.
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N IS THE NUMBER OF PAYMENTS
IN THE LOAN
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THAT WOULD BE 30 x 12 OR 360.
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THE INTEREST RATE IS 5.5%.
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EV IS THE PRESENT VALUE
OF THE LOAN,
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WHICH IS THE LOAN AMOUNT
OF $139,500.
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WE'LL COME BACK TO THE PAYMENT.
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THE FUTURE VALUE WOULD BE 0
AFTER THE LOAN IS PAID.
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PAYMENTS PER YEAR IS 12,
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NUMBER OF COMPOUNDS PER YEAR
IS ALSO 12.
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PAYMENTS ARE MADE
AT THE END OF THE MONTH.
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SO NOW WE'LL GO BACK UP TO PMT
FOR PAYMENT.
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WE'RE GOING TO CLEAR THIS
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AND NOW WE'RE GOING
TO PRESS ALPHA, ENTER FOR SOLVE.
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SO ALPHA, ENTER, VERIFIES THAT
OUR MONTHLY PAYMENT WOULD BE
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$792.07 ROUNDED
TO THE NEAREST CENT.
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REMEMBER WE ALSO ROUNDED
OUR DENOMINATOR HERE.
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AND NOW FOR THE LAST QUESTION
WE'RE GOING TO DETERMINE
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HOW MUCH INTEREST IS PAID
OVER THE LIFE OF THE LOAN.
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LET'S FIRST DETERMINE THE AMOUNT
PAID OVER THE LIFE OF THE LOAN.
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THAT WOULD BE THE MONTHLY
PAYMENT,
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WHICH IS $792.07 x THE NUMBER
OF MONTHS OVER 30 YEARS.
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SO THIS WOULD BE x 30 x 12.
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SO WE HAVE $792.07 x 360,
OR IF WE WANT 30 x 12,
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SO OVER 30 YEARS A TOTAL
OF $285,145.20 WILL BE PAID.
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WELL, REMEMBER THE LOAN AMOUNT,
OR THE AMOUNT BORROWED,
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WAS $139,500.
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SO THE DIFFERENCE OF THESE
TWO AMOUNTS
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WOULD BE THE AMOUNT OF INTEREST
PAID.
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SO WE'LL GO AHEAD AND TAKE
THIS AMOUNT HERE
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AND SUBTRACT THE LOAN AMOUNT
$139,500.
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SO $145,645.20 IS THE AMOUNT OF
INTEREST PAID OVER THE 30 YEARS.
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NOTICE THE AMOUNT OF INTEREST
PAID
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IS ACTUALLY MORE THAN
THE ORIGINAL LOAN AMOUNT.
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I HOPE YOU FOUND THIS EXAMPLE
HELPFUL.
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THE NEXT EXAMPLE WE'LL TAKE
A LOOK AT A LOAN
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THAT ALSO HAS POINTS.
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