Determining the Monthly Payment of an Installment Loan on the TI84


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

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