- WELCOME TO A VIDEO ON SIMPLE INTEREST.
THE GOAL OF THE VIDEO IS TO USE THE SIMPLE INTEREST FORMULA
TO ANSWER A VARIETY OF INTEREST QUESTIONS.
NOW, EVEN THOUGH MOST BANKS USE SOMETHING
CALLED COMPOUNDED INTEREST,
THE SIMPLE INTEREST FORMULA IS A NICE WAY
TO DEVELOP AN UNDERSTANDING
OF HOW INTEREST AFFECTS THE EARNINGS ON AN INVESTMENT
OR SAVINGS ACCOUNT,
OR HOW INTEREST WILL AFFECT HOW YOU PAY BACK A LOAN.
INTEREST REPRESENTS A CHANGE IN MONEY.
SO IF YOU HAVE A SAVINGS ACCOUNT OR INVESTMENT ACCOUNT,
INTEREST WILL INCREASE YOUR BALANCE
BASED UPON THE INTEREST RATE PAID BY THE BANK.
AND IF YOU HAVE A LOAN,
THE INTEREST WILL INCREASE THE AMOUNT YOU OWE
BASED UPON THE INTEREST RATE CHARGED BY THE BANK.
THE SIMPLE INTEREST FORMULA IS "I" = P x R x T,
WHERE "I" IS THE INTEREST,
P IS THE PRINCIPAL OR STARTING AMOUNT,
R IS THE RATE EXPRESSED AS A DECIMAL,
AND T IS TIME EXPRESSED IN YEARS.
LET'S GO AHEAD AND TAKE A LOOK AT SOME EXAMPLES.
IF YOU INVEST $3,500 IN A SAVINGS ACCOUNT
THAT PAYS 4% SIMPLE INTEREST,
HOW MUCH INTEREST WILL YOU EARN AFTER THREE YEARS
AND WHAT WILL THE NEW BALANCE BE?
SO FOR THIS SITUATION WE'RE TRYING TO FIND "I,"
OR THE INTEREST.
P, THE PRINCIPAL OR STARTING AMOUNT, WOULD BE $3,500.
R IS THE RATE OF RETURN, SO 4 IS 4%,
BUT IT MUST BE EXPRESSED AS A DECIMAL, SO THIS WOULD BE 0.04.
AND THEN T IS TIME IN YEARS, SO T = 3 YEARS.
WE HAVE ALL THE INFORMATION WE NEED
TO DETERMINE THE AMOUNT OF INTEREST
THAT'S EARNED IN THIS ACCOUNT.
THE INTEREST = $3,500, THE PRINCIPAL,
x THE RATE OF RETURN AS A DECIMAL, 0.04,
x THE TIME IN YEARS, WHICH = 3.
SO THIS PRODUCT WILL GIVE US OUR TOTAL INTEREST
OVER THE THREE YEARS.
SO WE HAVE 3,500 x .04 x 3.
SO THE INTEREST EARNED WILL BE $420.
BUT THEY ALSO ASK US
WHAT THE NEW BALANCE OF THE ACCOUNT WILL BE.
SO WE TAKE OUR STARTING AMOUNT, 3,500,
AND SO THIS INTEREST REPRESENTS THE INCREASE IN THE BALANCE.
SO WE ADD $420, AND SO THE ENDING BALANCE WILL BE $3,920.
SO, AGAIN, WE FOUND THE INTEREST EARNED,
AND THEN WE ALSO FOUND THE NEW BALANCE OF THE SAVINGS ACCOUNT
AFTER THREE YEARS.
LET'S GO AHEAD AND TAKE A LOOK AT ANOTHER EXAMPLE.
YOU BORROW $6,000 FROM A LOAN SHARK.
IF YOU WILL OWE $7,200 IN 18 MONTHS,
WHAT WOULD BE THE SIMPLE INTEREST RATE?
SO NOW WE'RE TRYING TO FIND THE INTEREST RATE, OR R,
SO WE SHOULD BE ABLE TO DETERMINE "I," P, AND T.
LET'S SEE IF WE CAN DO THAT.
REMEMBER, "I" REPRESENTS THE AMOUNT OF INTEREST.
SO IF YOU BORROWED $6,000 AND THEN YOU OWE $7,200,
THE DIFFERENCE WOULD REPRESENT THE AMOUNT OF INTEREST.
SO THE INTEREST IS GOING TO BE 7,200 - 6,000.
SO OUR INTEREST = $1,200.
P REPRESENTS THE PRINCIPAL OR STARTING AMOUNT--
THE LOAN AMOUNT WAS $6,000,
AND WE'RE TRYING TO SOLVE FOR THE INTEREST RATE.
NOW, OUR TIME IS 18 MONTHS,
BUT REMEMBER THE TIME HAS TO BE EXPRESSED IN YEARS.
WELL, SINCE 18 MONTHS IS 12 MONTHS + 6 MONTHS,
18 MONTHS = 1 1/2 YEARS, OR 1.5 YEARS.
SO IT IS IMPORTANT THAT WE DO HAVE TO HAVE OUR TIME
IN TERMS OF YEARS.
SO LET'S GO AHEAD AND SET THIS UP
AND SEE IF WE CAN SOLVE FOR R.
"I," WHICH IS 1,200, MUST = P, WHICH IS 6,000 x R,
WHICH WE'RE SOLVING FOR x T = 1.5 YEARS.
LET'S GO AHEAD AND SIMPLIFY THE RIGHT SIDE.
6,000 x 1.5 = 9,000, SO WE'LL HAVE 1,200 = 9,000R.
NOW WE'LL DIVIDE BOTH SIDES BY 9,000
TO DETERMINE OUR INTEREST RATE.
SO WE HAVE 1,200 DIVIDED BY 9,000.
NOW THIS IS OUR INTEREST RATE EXPRESSED AS A DECIMAL.
SO TO CONVERT A DECIMAL TO A PERCENTAGE,
REMEMBER WE CAN MULTIPLY IT BY 100.
SO THE INTEREST RATE IS ACTUALLY 13.3 REPEATING OR 13 1/3%.
OKAY. THAT'S GOING TO DO IT FOR SIMPLE INTEREST.
THANK YOU FOR WATCHING.