- AT THE AGE OF 28 YOU GET A PROMOTION TO VP OF MARKETING.
THE JOB HAS A SALARY OF $80,000 PER YEAR.
ASSUME A 2% CONTINUOUS INTEREST RATE.
IF YOU PLAN TO RETIRE AT 62
DETERMINE THE FUTURE VALUE AND PRESENT VALUE
OF THIS CONTINUOUS CASH FLOW.
SO WE'VE ALREADY DONE EXAMPLES
OF FUTURE VALUE AND PRESENT VALUE OF CONTINUOUS CASH FLOWS
AND WE'VE DONE THESE BY HAND.
SO FOR THIS EXAMPLE
WE'LL DETERMINE THESE VALUES ON THE CALCULATOR
AND THEN INTERPRET THE MEANING.
THE FIRST THING WE SHOULD DETERMINE ON THIS EXAMPLE
IS WHAT IS THE TIME GOING TO BE IN YEARS.
WELL, IF YOU'RE GOING TO WORK FROM 28 TO 62
WE'LL HAVE TO DETERMINE THE DIFFERENCE
TO KNOW HOW MANY YEARS YOU'LL BE WORKING.
SO 62 - 28 = 34.
SO FOR THE LIMITS OF INTEGRATION
WE'LL INTEGRATE FROM 0 TO 34 IN BOTH CASES.
SO THE FUTURE VALUE IS GOING TO BE EQUAL TO THE INTEGRAL
FROM 0 TO 34 OF R OF T
WHICH IS OUR CONTINUOUS MONEY FLOW OF $80,000 PER YEAR
x E RAISE TO THE POWER OF K x T
WHERE K IS THE INTEREST RATE EXPRESSED AS A DECIMAL.
SO WE'LL HAVE 0.02T, DT.
AND NOW FOR THE SET UP FOR PRESENT VALUE
IT'S ALMOST EXACTLY THE SAME
EXCEPT NOTICE HOW WE'LL HAVE -KT AS OUR EXPONENT.
AND NOW WE'LL DO THIS ON THE CALCULATOR.
AGAIN, IF YOU WANT TO SEE THEM BY HAND
YOU CAN SEE THE PREVIOUS VIDEOS.
SO IF WE PRESS MATH AND THEN SCROLL UP TO OPTION 9,
FUNCTION INTEGRATION, PRESS ENTER
AND NOW WE CAN JUST TYPE IN THE INTEGRAND 80,000.
SECOND NATURAL LOG BRINGS UP E RAISE TO THE POWER
AND WE HAVE 0.02 x T BUT I'M GOING TO USE X.
I CLOSE PARENTHESIS, X,
THE LIMITS OF INTEGRATION ARE FROM 0, 34.
SO THE FUTURE VALUE OF THIS CONTINUOUS CASH FLOW
WOULD BE $3,895,510.93.
SO WHAT THIS AMOUNT REPRESENTS
IS WE WERE TO TAKE ALL THE MONEY THAT WE EARNED FROM AGE 28 TO 62
AND PUT IT INTO AN INVESTMENT ACCOUNT
THAT EARNED 2% CONTINUOUS INTEREST AT OUR RETIREMENT AGE
WE WOULD HAVE THIS AMOUNT OF MONEY.
OF COURSE, WE WOULDN'T BE ABLE TO SAVE ALL THIS MONEY
BECAUSE WE HAVE TO LIVE BUT THIS IS WHAT THIS NUMBER REPRESENTS.
NOW TO DETERMINE THE PRESENT VALUE.
SO IF WE ALREADY HAD THIS IN THE CALCULATOR
WE COULD JUST PRESS SECOND ENTER
AND THEN WE CAN ACTUALLY EDIT WHAT WE'VE TYPED IN HERE.
SO WE JUST HAVE TO GO UP AND CHANGE THE EXPONENT
TO -0.02 x X.
SO IF WE SCROLL UP HERE AND THEN PRESS SECOND DELETE FOR INSERT
AND THEN THE NEGATIVE KEY WE SAVE OURSELVES A LOT OF TYPING.
AND NOW WE CAN JUST PRESS ENTER.
AND THE PRESENT VALUE OF THIS CONTINUOUS CASH FLOW
IS $1,973,532.03.
THIS VALUE REPRESENTS THE ONE TIME DEPOSIT
WE'D HAVE TO MAKE TODAY
IN THE SAME TYPE OF ACCOUNT TO HAVE THE SAME BALANCE
AS THE FUTURE VALUE AT THE AGE OF 62.