馃攳
Determining The Value of an Annuity on the TI84 - YouTube
Channel: Mathispower4u
[0]
- WELCOME TO A LESSON
ON DETERMINING THE VALUE
[2]
OF AN ANNUITY ON THE TI-84
GRAPHING CALCULATOR.
[6]
THE GOALS OF THE VIDEO
ARE TO DEFINE ANNUITY,
[8]
AND THEN ALSO DETERMINE
THE VALUE OF ANNUITY
[10]
ON THE CALCULATOR.
[12]
NOW, I DO HAVE ANOTHER VIDEO
[13]
THAT SHOWS HOW TO USE
THE FORMULA BY HAND
[15]
TO DETERMINE THE VALUE
OF ANNUITY.
[17]
BUT THIS VIDEO WILL FOCUS
[18]
ONLY ON USING THE GRAPHING
CALCULATOR.
[21]
AN ANNUITY IS A SEQUENCE
OF EQUAL PAYMENTS
[23]
MADE AT EQUAL TIME INTERVALS.
[25]
AN EXAMPLE WOULD BE AN IRA, OR
INDIVIDUAL RETIREMENT ACCOUNT,
[28]
WHERE FOR EXAMPLE YOU MAKE
MONTHLY DEPOSITS INTO AN ACCOUNT
[32]
IN HOPES OF ACCUMULATING
ENOUGH MONEY TO RETIRE SOME DAY.
[35]
THE VALUE OF AN ANNUITY
IS THE SUM OF ALL THE DEPOSITS
[38]
WITH ALL THE INTEREST EARNED.
[40]
THIS VIDEO WILL ONLY ADDRESS
ORDINARY ANNUITIES
[43]
WHEN THE PAYMENTS WERE MADE
AT THE END OF EACH PERIOD.
[46]
IF THE PAYMENTS WERE MADE
AT THE BEGINNING OF EACH PERIOD
[48]
IT'S CALLED AN ANNUITY DUE.
[51]
SO IN THE PREVIOUS VIDEO
WE USED THIS FORMULA HERE
[54]
TO DETERMINE THE VALUE
OF ANNUITY,
[56]
AND NOW WE'LL SHOW
HOW TO DO IT QUICKLY
[58]
ON THE GRAPHING CALCULATOR.
[60]
LET'S GO AHEAD AND TAKE A LOOK
AT OUR FIRST EXAMPLE.
[63]
LET'S SAY AT AGE 30 YOU DEPOSIT
$150 AT THE END OF EACH MONTH
[68]
INTO AN IRA THAT PAYS
4% INTEREST COMPOUNDED MONTHLY.
[72]
AT AGE 65 WHAT WILL THE VALUE
OF THE ANNUITY BE
[75]
AND HOW MUCH INTEREST
WOULD YOU HAVE EARNED?
[78]
SO LET'S GET OUR CALCULATORS
OUT.
[81]
WE'RE GOING TO PRESS
THE APPS KEY, WHICH IS HERE,
[84]
AND WE'RE GOING TO SELECT
THE FINANCE MENU.
[86]
SO WE'RE GOING TO PRESS ENTER.
[88]
THEN WE'RE GOING TO SELECT
THE TMV SOLVER,
[91]
SO WE'RE GOING TO PRESS ENTER
AGAIN.
[93]
NOW, THERE ARE A COUPLE WAYS
TO SOLVE THIS ON THE CALCULATOR,
[96]
BUT I LIKE USING THE TMV SOLVER.
[99]
WHAT WE'RE GOING TO DO HERE
IS ENTER IN ALL THE VALUES
[101]
EXCEPT FOR FV FOR FUTURE VALUE.
[105]
SO N REPRESENTS THE TOTAL NUMBER
OF COMPOUNDS OVER THE 35 YEARS,
[110]
35 YEARS BECAUSE WE'RE STARTING
AT 30 AND ENDING AT AGE 65.
[114]
SO THE NUMBER OF COMPOUNDS
PER YEAR IS 12
[117]
BECAUSE IT'S COMPOUNDED MONTHLY.
[119]
SO N IS GOING TO BE 12 x 35.
[124]
"I" STANDS FOR THE INTEREST
RATE, WHICH IS 4%.
[128]
PRESENT VALUE WHEN WE START
WOULD BE ZERO
[131]
BECAUSE THERE'S NO MONEY
IN THE ACCOUNT TO BEGIN WITH.
[135]
THE PAYMENT IS THE AMOUNT THAT
WE'RE GOING TO PAY EACH MONTH
[137]
WHICH WILL BE $150.
[139]
BUT SINCE WE'RE PAYING IT,
WE'RE GOING TO TYPE IN -150.
[144]
WE'LL LEAVE THE FUTURE VALUE
ALONE FOR RIGHT NOW
[147]
AND SCROLL DOWN TO P/N.
[150]
THAT STANDS FOR PAYMENTS
PER YEAR.
[152]
SINCE IT'S MONTHLY
THAT'LL BE 12.
[156]
C/YEAR STANDS FOR COMPOUNDS
PER YEAR, THAT'LL BE 12 AS WELL.
[164]
AND, AS WE MENTIONED BEFORE,
[165]
WE'RE GOING TO PAYMENTS
AT THE END OF EACH MONTH.
[167]
NOW LET'S GO BACK UP TO FV
FOR FUTURE VALUE.
[171]
WITH OUR CURSOR HERE
WE'RE GOING TO CLEAR THIS VALUE.
[174]
IF WE PRESS ALPHA, ENTER IT WILL
SOLVE FOR THE FUTURE VALUE GIVEN
[178]
WHAT WE'VE ENTERED.
[180]
SO THE FUTURE VALUE WILL BE
$137,059.64 APPROXIMATELY.
[186]
LET'S GO AHEAD
AND WRITE THAT DOWN.
[192]
NOW LET'S TALK ABOUT
THE SECOND QUESTION
[193]
THAT ASK HOW MUCH INTEREST
WOULD YOU EARN.
[196]
WELL, THE INTEREST EARNED WOULD
BE EQUAL TO THE ACCOUNT BALANCE
[199]
MINUS ALL OF THE DEPOSITS.
[203]
SO WE TAKE THE BALANCE
OF THE ACCOUNT
[210]
AND THEN WE SUBTRACT
ALL OF OUR DEPOSITS.
[213]
WELL, EACH DEPOSIT WAS $150,
[216]
SO x 12 WOULD GIVE US THE AMOUNT
OF THE YEARLY DEPOSITS.
[221]
AND THEN WE MAKE THESE DEPOSITS
FOR 35 YEARS, SO x 35.
[228]
SO THIS ACCOUNT WOULD'VE EARNED
$74,059.64 OVER THE 35 YEARS.
[243]
NOW LET'S TAKE A LOOK
AT THE SECOND EXAMPLE
[245]
WHERE IT'S THE SAME PROBLEM,
[246]
BUT INSTEAD OF STARTING
AT AGE 30,
[249]
HOW WOULD IT AFFECT THE BALANCE
IF YOU STARTED AT AGE 40?
[252]
SO IF WE GO BACK
TO OUR CALCULATOR
[254]
AND YOU WANT TO PRESS APPS,
ENTER, ENTER.
[261]
AND NOW WE'RE GOING TO HAVE
TO CHANGE THE VALUE OF N
[262]
BECAUSE NOW WE'RE ONLY MAKING
DEPOSITS FOR 25 YEARS.
[266]
SO N IS GOING TO BE 12 x 25.
[274]
EVERYTHING ELSE SHOULD REMAIN
THE SAME, 4% INTEREST,
[278]
A ZERO PRESENT VALUE,
A PAYMENT OF $150 PER MONTH,
[282]
12 PAYMENTS PER YEAR,
AND 12 COMPOUNDS PER YEAR.
[285]
SO LET'S GO DOWN TO FUTURE
VALUE, WE'LL CLEAR THIS,
[290]
AND PRESS ALPHA, ENTER.
[292]
AND NOW THE BALANCE AT AGE 65
WOULD ONLY BE $77,119.43.
[306]
AND LET'S GO AHEAD AND FIGURE
OUT HOW MUCH INTEREST WAS EARNED
[308]
IN THIS SITUATION.
[310]
GO BACK TO THE HOME SCREEN,
2ND QUIT.
[313]
SO STARTING WITH THE BALANCE
OF THE ANNUITY AT AGE 65,
[322]
WE'LL SUBTRACT THE TOTAL
DEPOSITS INTO THE ACCOUNT.
[326]
SO EACH DEPOSIT IS $150 x 12
FOR EACH YEAR,
[332]
AND THEN FOR 25 YEARS, SO x 25.
[336]
THIS WILL GIVE US THE TOTAL
AMOUNT OF INTEREST EARNED,
[339]
WHICH IS $32,119.43.
[347]
SO MAYBE THE OUTCOME
IS A LITTLE BIT SURPRISING.
[349]
IF WE STARTED AT AGE 40
THE ANNUITY WOULD HAVE A VALUE
[352]
OF LITTLE OVER 77,000,
[355]
AND WE WOULD HAVE EARNED
OVER $32,000 OF INTEREST.
[358]
BUT IF WE START JUST 10 YEARS
EARLIER
[361]
THE VALUE WOULD BE MUCH HIGHER
AT 177,000,
[364]
AND WE WOULD'VE EARNED
OVER $74,000 OF INTEREST
[368]
OR MORE THAN TWICE THE INTEREST
OVER THE EXTRA 10 YEARS.
[372]
I HOPE YOU FOUND THESE EXAMPLES
HELPFUL.
[373]
THANK YOU FOR WATCHING.
Most Recent Videos:
You can go back to the homepage right here: Homepage