- WELCOME TO A LESSON ON DETERMINING THE VALUE
OF AN ANNUITY ON THE TI-84 GRAPHING CALCULATOR.
THE GOALS OF THE VIDEO ARE TO DEFINE ANNUITY,
AND THEN ALSO DETERMINE THE VALUE OF ANNUITY
ON THE CALCULATOR.
NOW, I DO HAVE ANOTHER VIDEO
THAT SHOWS HOW TO USE THE FORMULA BY HAND
TO DETERMINE THE VALUE OF ANNUITY.
BUT THIS VIDEO WILL FOCUS
ONLY ON USING THE GRAPHING CALCULATOR.
AN ANNUITY IS A SEQUENCE OF EQUAL PAYMENTS
MADE AT EQUAL TIME INTERVALS.
AN EXAMPLE WOULD BE AN IRA, OR INDIVIDUAL RETIREMENT ACCOUNT,
WHERE FOR EXAMPLE YOU MAKE MONTHLY DEPOSITS INTO AN ACCOUNT
IN HOPES OF ACCUMULATING ENOUGH MONEY TO RETIRE SOME DAY.
THE VALUE OF AN ANNUITY IS THE SUM OF ALL THE DEPOSITS
WITH ALL THE INTEREST EARNED.
THIS VIDEO WILL ONLY ADDRESS ORDINARY ANNUITIES
WHEN THE PAYMENTS WERE MADE AT THE END OF EACH PERIOD.
IF THE PAYMENTS WERE MADE AT THE BEGINNING OF EACH PERIOD
IT'S CALLED AN ANNUITY DUE.
SO IN THE PREVIOUS VIDEO WE USED THIS FORMULA HERE
TO DETERMINE THE VALUE OF ANNUITY,
AND NOW WE'LL SHOW HOW TO DO IT QUICKLY
ON THE GRAPHING CALCULATOR.
LET'S GO AHEAD AND TAKE A LOOK AT OUR FIRST EXAMPLE.
LET'S SAY AT AGE 30 YOU DEPOSIT $150 AT THE END OF EACH MONTH
INTO AN IRA THAT PAYS 4% INTEREST COMPOUNDED MONTHLY.
AT AGE 65 WHAT WILL THE VALUE OF THE ANNUITY BE
AND HOW MUCH INTEREST WOULD YOU HAVE EARNED?
SO LET'S GET OUR CALCULATORS OUT.
WE'RE GOING TO PRESS THE APPS KEY, WHICH IS HERE,
AND WE'RE GOING TO SELECT THE FINANCE MENU.
SO WE'RE GOING TO PRESS ENTER.
THEN WE'RE GOING TO SELECT THE TMV SOLVER,
SO WE'RE GOING TO PRESS ENTER AGAIN.
NOW, THERE ARE A COUPLE WAYS TO SOLVE THIS ON THE CALCULATOR,
BUT I LIKE USING THE TMV SOLVER.
WHAT WE'RE GOING TO DO HERE IS ENTER IN ALL THE VALUES
EXCEPT FOR FV FOR FUTURE VALUE.
SO N REPRESENTS THE TOTAL NUMBER OF COMPOUNDS OVER THE 35 YEARS,
35 YEARS BECAUSE WE'RE STARTING AT 30 AND ENDING AT AGE 65.
SO THE NUMBER OF COMPOUNDS PER YEAR IS 12
BECAUSE IT'S COMPOUNDED MONTHLY.
SO N IS GOING TO BE 12 x 35.
"I" STANDS FOR THE INTEREST RATE, WHICH IS 4%.
PRESENT VALUE WHEN WE START WOULD BE ZERO
BECAUSE THERE'S NO MONEY IN THE ACCOUNT TO BEGIN WITH.
THE PAYMENT IS THE AMOUNT THAT WE'RE GOING TO PAY EACH MONTH
WHICH WILL BE $150.
BUT SINCE WE'RE PAYING IT, WE'RE GOING TO TYPE IN -150.
WE'LL LEAVE THE FUTURE VALUE ALONE FOR RIGHT NOW
AND SCROLL DOWN TO P/N.
THAT STANDS FOR PAYMENTS PER YEAR.
SINCE IT'S MONTHLY THAT'LL BE 12.
C/YEAR STANDS FOR COMPOUNDS PER YEAR, THAT'LL BE 12 AS WELL.
AND, AS WE MENTIONED BEFORE,
WE'RE GOING TO PAYMENTS AT THE END OF EACH MONTH.
NOW LET'S GO BACK UP TO FV FOR FUTURE VALUE.
WITH OUR CURSOR HERE WE'RE GOING TO CLEAR THIS VALUE.
IF WE PRESS ALPHA, ENTER IT WILL SOLVE FOR THE FUTURE VALUE GIVEN
WHAT WE'VE ENTERED.
SO THE FUTURE VALUE WILL BE $137,059.64 APPROXIMATELY.
LET'S GO AHEAD AND WRITE THAT DOWN.
NOW LET'S TALK ABOUT THE SECOND QUESTION
THAT ASK HOW MUCH INTEREST WOULD YOU EARN.
WELL, THE INTEREST EARNED WOULD BE EQUAL TO THE ACCOUNT BALANCE
MINUS ALL OF THE DEPOSITS.
SO WE TAKE THE BALANCE OF THE ACCOUNT
AND THEN WE SUBTRACT ALL OF OUR DEPOSITS.
WELL, EACH DEPOSIT WAS $150,
SO x 12 WOULD GIVE US THE AMOUNT OF THE YEARLY DEPOSITS.
AND THEN WE MAKE THESE DEPOSITS FOR 35 YEARS, SO x 35.
SO THIS ACCOUNT WOULD'VE EARNED $74,059.64 OVER THE 35 YEARS.
NOW LET'S TAKE A LOOK AT THE SECOND EXAMPLE
WHERE IT'S THE SAME PROBLEM,
BUT INSTEAD OF STARTING AT AGE 30,
HOW WOULD IT AFFECT THE BALANCE IF YOU STARTED AT AGE 40?
SO IF WE GO BACK TO OUR CALCULATOR
AND YOU WANT TO PRESS APPS, ENTER, ENTER.
AND NOW WE'RE GOING TO HAVE TO CHANGE THE VALUE OF N
BECAUSE NOW WE'RE ONLY MAKING DEPOSITS FOR 25 YEARS.
SO N IS GOING TO BE 12 x 25.
EVERYTHING ELSE SHOULD REMAIN THE SAME, 4% INTEREST,
A ZERO PRESENT VALUE, A PAYMENT OF $150 PER MONTH,
12 PAYMENTS PER YEAR, AND 12 COMPOUNDS PER YEAR.
SO LET'S GO DOWN TO FUTURE VALUE, WE'LL CLEAR THIS,
AND PRESS ALPHA, ENTER.
AND NOW THE BALANCE AT AGE 65 WOULD ONLY BE $77,119.43.
AND LET'S GO AHEAD AND FIGURE OUT HOW MUCH INTEREST WAS EARNED
IN THIS SITUATION.
GO BACK TO THE HOME SCREEN, 2ND QUIT.
SO STARTING WITH THE BALANCE OF THE ANNUITY AT AGE 65,
WE'LL SUBTRACT THE TOTAL DEPOSITS INTO THE ACCOUNT.
SO EACH DEPOSIT IS $150 x 12 FOR EACH YEAR,
AND THEN FOR 25 YEARS, SO x 25.
THIS WILL GIVE US THE TOTAL AMOUNT OF INTEREST EARNED,
WHICH IS $32,119.43.
SO MAYBE THE OUTCOME IS A LITTLE BIT SURPRISING.
IF WE STARTED AT AGE 40 THE ANNUITY WOULD HAVE A VALUE
OF LITTLE OVER 77,000,
AND WE WOULD HAVE EARNED OVER $32,000 OF INTEREST.
BUT IF WE START JUST 10 YEARS EARLIER
THE VALUE WOULD BE MUCH HIGHER AT 177,000,
AND WE WOULD'VE EARNED OVER $74,000 OF INTEREST
OR MORE THAN TWICE THE INTEREST OVER THE EXTRA 10 YEARS.
I HOPE YOU FOUND THESE EXAMPLES HELPFUL.
THANK YOU FOR WATCHING.