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Determining the Monthly Payment of an Installment Loan on the TI84 - YouTube
Channel: Mathispower4u
[1]
- WELCOME TO A LESSON ON USING
THE TI84 GRAPHING CALCULATOR
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TO DETERMINE A LOAN PAYMENT.
[6]
THE GOAL OF THE VIDEO IS TO
DETERMINE THE LOAN PAYMENT
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FOR A FIXED INSTALLMENT LOAN
ON THE TI84.
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INSTALLMENT BUYING IS WHEN YOU
PURCHASE SOMETHING TODAY
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WITH A LOAN
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THAT YOU PAY BACK
WITH EQUAL PAYMENTS
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OVER A REGULAR PERIOD OF TIME,
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USUALLY MONTHLY
OVER A PERIOD OF YEARS.
[22]
THE TWO MOST COMMON EXAMPLES
WOULD BE A CAR LOAN
[25]
AND A HOME MORTGAGE LOAN.
[27]
IN THE PREVIOUS VIDEO WE USED
THIS LOAN PAYMENT FORMULA
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WITH FIXED PAYMENTS
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TO DETERMINE IN MOST CASES
THE MONTHLY PAYMENT.
[35]
IN THIS VIDEO WE'LL USE
THE FINANCE MENU
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OF THE GRAPHING CALCULATOR
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TO ANSWER THE SAME QUESTIONS
MUCH QUICKER
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USING THE GRAPHING CALCULATOR.
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AND IT'S REALLY A NICE FEATURE
OF THE GRAPHING CALCULATOR
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TO PLAY AROUND WITH BEFORE
CONSIDERING TAKING OUT A LOAN.
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SO LET'S GO AND TAKE A LOOK
AT OUR FIRST EXAMPLE.
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HERE WE'RE GOING TO DETERMINE
THE MONTHLY PAYMENT
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FOR A 30 YEAR MORTGAGE LOAN
OF $150,000
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WITH A 5% FIXED INTEREST
COMPOUNDED MONTHLY.
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AND THEN WE'LL DETERMINE THE
TOTAL AMOUNT OF INTEREST PAID
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OVER THE 30 YEARS.
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SO WE'RE GOING TO PRESS
THE APPS KEY,
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AND THEN PRESS ENTER
TO ACCESS THE FINANCE MENU.
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AND THEN WE'RE GOING TO PRESS
ENTER AGAIN
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TO ACCESS THE PMV SOLVER.
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CAPITAL "N" REPRESENTS
THE TOTAL NUMBER OF PAYMENTS
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THAT WILL BE MADE.
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WE'RE MAKING MONTHLY PAYMENTS
OVER 30 YEARS,
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SO N WOULD BE 12 x 30 OR 360.
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"I" REPRESENTS THE INTEREST RATE
WHICH IS 5%.
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PV REPRESENTS THE PRESENT VALUE
OF THE LOAN THAT'S $150,000.
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WE'LL COME BACK
TO THE PAYMENT AMOUNT.
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THE FUTURE VALUE WHEN THE LOAN
IS PAID OFF SHOULD BE $0.00.
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AND P/Y REPRESENTS THE NUMBER
OF PAYMENTS PER YEAR.
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WE'RE PAYING MONTHLY
SO IT'S GOING TO BE 12.
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AND THEN C/Y MEANS
COMPOUNDS PER YEAR.
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IT'S COMPOUNDED MONTHLY
SO THIS IS ALSO 12.
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AND NOW ALL WE HAVE TO DO IS GO
BACK UP TO THE PAYMENT CELL.
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WE'RE GOING TO CLEAR THIS AMOUNT
AND THEN PRESS ALPHA, ENTER,
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AND IT WILL TELL US
THE REQUIRED MONTHLY PAYMENT.
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AND NOTICE THAT IT'S NEGATIVE
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BECAUSE WE'LL BE PAYING
THAT AMOUNT.
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SO THE PAYMENT WOULD BE $805.23
PER MONTH.
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NOW LET'S ANSWER THE SECOND
QUESTION THAT ASKED US
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HOW MUCH INTEREST WILL BE PAID
OVER THE 30 YEARS.
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SO WE'LL GO TO THE HOME SCREEN
BY PRESSING SECOND MODE
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FOR SECOND QUIT.
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SO OUR LOAN AMOUNT OF $805.23
WILL BE PAID
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A TOTAL OF 360 TIMES
OR 12 TIMES A YEAR FOR 30 YEARS.
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SO THIS REPRESENTS THE TOTAL
AMOUNT PAID OVER THE 30 YEARS.
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AND IF WE SUBTRACT OUT
THE LOAN AMOUNT
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THAT'LL LEAVE US WITH THE AMOUNT
OF INTEREST PAID.
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SO - $150,000 LEAVES US WITH
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$139,882.80 WORTH OF
INTEREST PAID.
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SO WE'D BE PAYING ALMOST AS MUCH
INTEREST AS THE LOAN AMOUNT
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OVER THE 30 YEAR PERIOD.
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NOW FOR OUR SECOND EXAMPLE
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WE'RE GOING TO LOOK AT
THE SAME SITUATION,
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BUT INSTEAD OF USING
A 30 YEAR MORTGAGE
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WE'LL TAKE A LOOK AT
THE DIFFERENCE
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IF WE USE A 15 YEAR MORTGAGE.
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SO WE'RE GOING TO PRESS THE APPS
KEY AGAIN,
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ENTER AT THE FINANCE MENU,
ENTER FOR PMV SOLVER.
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NOW ALL THIS INFORMATION
IS GOING TO BE THE SAME,
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BUT NOW N, THE TOTAL NUMBER
OF PAYMENTS,
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IS GOING TO BE 12 x 15
INSTEAD OF 12 x 30
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BECAUSE IT'S A 15 YEAR MORTGAGE.
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AND, AGAIN, EVERYTHING ELSE
IS GOING TO STAY THE SAME
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SO WE'LL GO DOWN TO THE PAYMENT
CELL, CLEAR THIS AMOUNT,
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AND THEN JUST PRESS ALPHA, ENTER
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TO DETERMINE
THE NEW MONTHLY PAYMENT.
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AND NOW THE PAYMENT
WOULD BE $1,186.19.
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SO TO DETERMINE THE TOTAL
INTEREST PAID OVER 15 YEARS
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WE'LL TAKE THE MONTHLY PAYMENT,
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MULTIPLY IT BY 12 FOR THE NUMBER
OF PAYMENTS PER YEAR.
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THEN MULTIPLY IT BY 15
FOR 15 YEARS.
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SO THIS IS THE AMOUNT OF MONEY
PAID OVER THE 15 YEARS,
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MINUS THE LOAN AMOUNT WILL LEAVE
US WITH THE TOTAL INTEREST PAID.
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AND SO NOW THE AMOUNT
OF INTEREST PAID IS $63,514.20.
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SO OBVIOUSLY
FOR THE 15 YEAR MORTGAGE
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THE MONTHLY PAYMENT WENT UP
CONSIDERABLY,
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BUT THE AMOUNT OF INTEREST PAID
ALSO WENT DOWN CONSIDERABLY.
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SO IF YOU CAN AFFORD THE 15 YEAR
MORTGAGE
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YOU SAVE YOURSELF FROM PAYING
A LOT OF EXTRA INTEREST.
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LET'S GO AND TAKE A LOOK AT ONE
MORE EXAMPLE WITH A CAR LOAN.
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LET'S DETERMINE THE MONTHLY
PAYMENT
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FOR A FIVE YEAR CAR LOAN
OF $20,000
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WITH A 5.5% INTEREST
COMPOUNDED MONTHLY.
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AND THEN WE'LL ALSO DETERMINE
THE TOTAL INTEREST
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PAID OVER THE FIVE YEARS.
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AND, AGAIN, IT'S VERY QUICK
AND EASY TO DO
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ON THE GRAPHING CALCULATOR.
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WE'LL PRESS THE APPS KEY,
AND THEN ENTER FOR FINANCE,
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AND ENTER FOR PMV SOLVER.
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OUR CAPITAL "N" HERE IS GOING TO
BE 12 MONTHLY PAYMENTS
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FOR 5 YEARS
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OR 12 x 5, WHICH IS 60.
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INTEREST RATE IS 5.5%,
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THE PRESENT VALUE OF THE LOAN
IS $20,000.
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WE'LL COME BACK TO THIS ROW
IN JUST A MINUTE.
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FUTURE VALUE IS GOING TO BE
ZERO.
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PAYMENTS PER YEAR IS 12,
COMPOUNDS PER YEAR IS ALSO 12.
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SO WE'LL GO BACK UP TO THE
PAYMENT CELL, CLEAR THIS VALUE,
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AND PRESS ALPHA, ENTER.
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SO OUR MONTHLY CAR PAYMENT
WOULD BE $382.02.
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AND THEN, AGAIN,
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TO DETERMINE THE TOTAL AMOUNT
OF INTEREST PAID
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WE'D MULTIPLY OUR MONTHLY
PAYMENT x 12 x 5
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OR JUST 382.02 x 60.
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THIS IS THE TOTAL AMOUNT PAID,
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AND THEN WE'LL SUBTRACT OUT
THE LOAN AMOUNT OF $20,000.
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SO OVER THE FIVE YEAR PERIOD
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WE WOULD PAY $2,921.20
OF TOTAL INTEREST.
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AND THAT'S GOING TO DO IT
FOR THIS VIDEO.
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I HOPE YOU CAN TAKE ADVANTAGE
OF THIS TOOL
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ON THE GRAPHING CALCULATOR
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TO GATHER ALL THE INFORMATION
YOU NEED
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BEFORE TAKING OUT A LOAN.
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THANK YOU FOR WATCHING.
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