# Practice English Speaking&Listening with: Compounded Interest

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- MOST OF US HAVE EITHER A CHECKING OR SAVINGS ACCOUNT

THAT PAYS SOME FORM OF INTEREST.

MOST BANKS USE A FORMULA CALLED COMPOUNDED INTEREST

TO CALCULATE THE INTEREST THEY PAY YOU EACH MONTH.

THIS VIDEO WILL ADDRESS HOW YOU USE COMPOUNDED INTEREST

TO SOLVE INTEREST PROBLEMS.

LET'S TAKE A LOOK AT THE FORMULA FIRST.

HERE IT IS: IF A PRINCIPAL P IS INVESTED

AT AN INTEREST RATE I,

EXPRESSED AS A DECIMAL, AND COMPOUNDED N TIMES A YEAR,

IN T YEARS IT WILL GROW TO THE AMOUNT "A".

A REWORD OF THIS WITH MAYBE SOME SIMPLER LANGUAGE:

P IS THE STARTING AMOUNT OR THE INITIAL INVESTMENT,

I IS THE INTEREST RATE

THAT MUST BE EXPRESSED AS A DECIMAL.

REMEMBER TO CONVERT A PERCENTAGE TO A DECIMAL

WE MUST REMOVE THE PERCENTAGE SYMBOL AND DIVIDE BY 100.

N IS THE NUMBER OF COMPOUNDS PER YEAR.

SO IF IT'S COMPOUNDED QUARTERLY N WOULD BE 4,

SINCE THERE ARE 4 QUARTERS IN A YEAR.

COMPOUNDED MONTHLY, N WOULD BE 12, AND SO ON.

T IS TIME, BUT IT MUST BE IN YEARS.

SO OF COURSE IN TWO YEARS T WOULD BE 2.

BUT LET'S SAY THEY TOLD YOU TIME WAS 18 MONTHS.

18 MONTHS WOULD BE A YEAR AND A HALF OR 1.5 YEARS.

AND LASTLY, "A" IS THE AMOUNT AFTER THE GIVEN TIME.

LET'S TAKE A LOOK AT A COUPLE OF QUICK EXAMPLES.

SUPPOSE THAT YOU INVEST \$1000

AT 8% INTEREST COMPOUNDED QUARTERLY.

HOW MUCH IS IN THE ACCOUNT AT THE END OF 3 YEARS?

OKAY. LET'S SET THIS UP.

WHAT WOULD OUR PRINCIPAL BE?

AGAIN, PRINCIPAL IS THE STARTING AMOUNT

OR THE INITIAL INVESTMENT,

SO THAT'S \$1000 x THE QUANTITY OF 1 + I,

THE INTEREST RATE AS A DECIMAL.

8% AS A DECIMAL WOULD BE 0.08.

NOW THIS IS COMPOUNDED QUARTERLY, SO N WOULD BE 4,

AND THEN WE'RE RAISING THIS TO THE POWER OF N x T.

WELL, WE ALREADY SAID N IS 4.

T IS TIME IN YEARS, SO 3.

NOW LET'S TAKE A LOOK AT THIS FOR A MOMENT.

THIS MAY SEEM KIND OF ODD,

BUT ESSENTIALLY WHAT WE'RE DOING

IS WE'RE GETTING COMMON UNITS.

WHAT I MEAN BY THAT IS THIS:

IF WE TAKE 8% ANNUAL INTEREST RATE AND DIVIDE IT BY 4,

WE'RE ESSENTIALLY GETTING A QUARTERLY INTEREST RATE.

AND IF YOU MULTIPLY 4 x 3,

THAT WOULD BE THE NUMBER OF QUARTERS IN 3 YEARS.

SO ESSENTIALLY WHAT WE'RE DOING HERE

IS WE'RE PUTTING EVERYTHING IN QUARTERS.

OKAY, LET'S GO AHEAD AND GO TO THE CALCULATOR

AND SIMPLIFY THIS EXPRESSION ON THE RIGHT SIDE.

SO WE'RE GOING TO ENTER IT IN PRETTY MUCH JUST AS WE SEE IT.

1000 x THE QUANTITY 1 + .08 DIVIDED BY 4,

AND THAT'S GOING TO BE RAISED TO THE 4 x 3 POWER.

I'LL PUT 4 x 3 IN PARENTHESES,

OR OF COURSE I COULD JUST PUT 12.

AND THAT'S PRETTY MUCH ALL WE HAVE TO DO.

THIS GIVES US "A" OR THE AMOUNT AFTER 3 YEARS.

SO IT'S \$1268.24.

IT'S A PRETTY STRAIGHTFORWARD EXAMPLE

OF COMPOUNDED INTEREST.

NOW THE NEXT EXAMPLE WHAT I WANT TO DO

IS COMPARE WHAT IS GOING TO HAPPEN TO THIS BALANCE

IF WE CHANGE JUST ONE CONDITION.

WE'RE GOING TO CHANGE HOW OFTEN IT'S COMPOUNDED.

LET'S TAKE A LOOK AT WHAT ARE WE GOING TO DO

IF IT'S COMPOUNDED DAILY.

SAME STARTING AMOUNT, SAME INTEREST RATE,

SAME AMOUNT OF TIME, AND WE'LL SEE THE DIFFERENCE.

OKAY. SO LET'S WRITE OUT OUR FORMULA.

THE AMOUNT AFTER 3 YEARS WOULD BE EQUAL TO THE PRINCIPAL,

STILL \$1000 x THE QUANTITY 1

+ THE INTEREST RATE AS A DECIMAL,

AND LET'S DIVIDE THIS BY N.

IF IT'S COMPOUNDED DAILY

WE ASSUME THERE ARE 365 DAYS IN A YEAR,

AND WE RAISE THIS TO THE N x T POWER.

SO 365 DAYS x 3.

AGAIN, WE HAVE A DAILY RATE HERE,

AND WE HAVE THE NUMBER OF DAYS IN THREE YEARS HERE.

LET'S GO BACK TO OUR CALCULATOR

AND DETERMINE THIS AMOUNT.

YOU MIGHT BE THINKING WHICH WILL GIVE YOU MORE MONEY?

ONE NICE THING ABOUT THE GRAPHING CALCULATOR

IS INSTEAD OF RETYPING EVERYTHING THAT I JUST DID,

IF I HIT SECOND ENTER

IT BRINGS BACK THE LAST EXPRESSION,

EXCEPT NOW WHAT I CAN DO IS I CAN GO BACK

AND EDIT ANYTHING I WANT.

AND SO THE ONLY CHANGE IS FROM CHANGING THIS 4 TO 365.

NOW 4 IS A SINGLE DIGIT,

SO I CAN OVERWRITE THE 4 WITH THE 3,

AND NOW I HAVE TO INSERT THE 65.

SECOND DELETE IS THE INSERT, AND WE'LL GET THE 65.

OF COURSE I COULD JUST DELETE EVERYTHING AND RETYPE IT,

BUT I'M TRYING TO SAVE A LITTLE BIT OF WORK HERE.

AND I'LL DO THE SAME THING WITH THIS FOUR.

I'LL OVERWRITE THE 4 WITH THE 3,

AND THEN I'LL INSERT THE 65.

AND IF WE COMPARE THESE AMOUNTS,

THIS AMOUNT IS \$1271.22 ROUGHLY.

AS YOU CAN SEE, FROM THE PREVIOUS PROBLEM WE HAD \$1268,

SO THE AMOUNT HAS INCREASED.

AND HOPEFULLY THAT MAKES SENSE,

BECAUSE IF YOU'RE BEING PAID INTEREST ON A DAILY BASIS

THE MORE MONEY YOU WOULD GET PAID THE MORE OFTEN,

THE BETTER OFF YOU WOULD BE.

NOW THIS MAY NOT SEEM LIKE A BIG DIFFERENCE,

BUT OF COURSE IF YOU'RE DEALING

IN MILLIONS AND BILLIONS OR EVEN TRILLIONS OF DOLLARS