- WELCOME TO A LESSON ON SIMPLE INTEREST DISCOUNTED LOANS.
A DISCOUNTED LOAN IS A LOAN THAT COLLECTS INTEREST
FROM THE AMOUNT OF THE LOAN OR FACE VALUE OF THE LOAN
WHEN THE LOAN IS MADE.
THE INTEREST IS ADDUCTED FROM THE LOAN AMOUNT,
SO YOU DON'T ACTUALLY RECEIVE THE FULL LOAN AMOUNT
OR FACE VALUE OF THE LOAN WHEN YOU RECEIVE THE LOAN.
THE DEDUCTED INTEREST IS THE DISCOUNT.
FOR REVIEW, HERE'S THE SIMPLE INTEREST FORMULA
WHERE "I" IS THE INTEREST AMOUNT,
P IS THE PRINCIPLE OR STARTING AMOUNT OF THE LOAN,
R IS THE ANNUAL INTEREST RATE EXPRESSED AS A DECIMAL,
AND T IS TIME, WHICH MUST BE IN YEARS.
NOW, IT SHOULD BE NOTED
THAT SOMETIMES THERE ARE ADDITIONAL FEES
FOR DISCOUNTED LOANS.
LET'S TAKE A LOOK AT AN EXAMPLE.
LET'S SAY YOU BORROW $2,000 ON A 12% DISCOUNTED LOAN
FOR FOUR MONTHS.
NUMBER ONE, WE WANT TO DETERMINE WHAT IS THE LOAN DISCOUNT.
NUMBER TWO, WE WANT TO DETERMINE THE NET AMOUNT OF MONEY
YOU'LL ACTUALLY RECEIVE FROM THE LOAN.
AND THEN NUMBER THREE,
WHAT IS A LOAN'S ACTUAL ANNUAL SIMPLE INTEREST RATE?
SO, NUMBER ONE,
REMEMBER THE DISCOUNT IS THE INTEREST PAID UP FRONT,
SO WE'LL USE THE SIMPLE INTEREST RATE FORMULA.
SO FOR NUMBER ONE WE'LL HAVE "I"
OR THE DISCOUNT IS EQUAL TO P
THE LOAN AMOUNT WHICH IS $2,000 x R THE ANNUAL INTEREST RATE,
WHICH IS 12%.
12% EXPRESSED AS A FRACTION WOULD BE 12/100 OR 12-HUNDRETHS,
WHICH AS A DECIMAL WOULD BE 0.12.
SO WE HAVE x 0.12 x T, WHICH IS TIME IN YEARS.
NOTICE HOW THE TIME IS FOUR MONTHS.
WELL, FOUR MONTHS WOULD BE 4/12 OF A YEAR,
WHICH WOULD SIMPLIFY TO 1/3 IF WE WANT.
SO THIS PRODUCT WILL GIVE US OUR LOAN DISCOUNT
OR THE INTEREST AMOUNT THAT YOU WILL PAY UP FRONT.
SO WE HAVE 2,000 x 0.12 x 4/12, WHICH IS EQUIVALENT TO 1/3.
AGAIN, FOUR MONTHS IS 1/3 OF A YEAR.
SO THE LOAN DISCOUNT IS $80.
SO NOW FOR NUMBER TWO,
TO DETERMINE THE NET AMOUNT OF MONEY
THAT YOU WILL ACTUALLY RECEIVE,
IF THERE ARE NO OTHER FEES
THE NET AMOUNT THAT YOU'LL RECEIVE WOULD BE THE LOAN AMOUNT
$2,000 - THE DISCOUNT OF $80.
SO YOU ACTUALLY RECEIVE $1,920 FOR THIS DISCOUNTED LOAN.
AND NOW FOR THE LAST QUESTION WE WANT TO DETERMINE
WHAT IS THE LOAN'S ACTUAL ANNUAL SIMPLE INTEREST RATE
SINCE WE'RE ONLY RECEIVING 1,920,
BUT WE'RE PAYING 12% INTEREST ON $2,000.
SO USING OUR SIMPLE INTEREST FORMULA,
"I" THE INTEREST IS $80.
THIS TIME P, THE PRINCIPLE, IS ACTUALLY THE AMOUNT OF MONEY
THAT WE RECEIVE WHICH IS $1,920.
WE'RE TRYING TO FIND R THE SIMPLE INTEREST RATE,
SO THAT'S OUR UNKNOWN, TIMES T WHICH IS THE TIME IN YEARS.
SINCE IT'S FOUR MONTHS WE ALREADY SAID IT'S 4/12 OF A YEAR
WHICH SIMPLIFIES TO 1/3.
AND NOW IF WE SOLVE THIS FOR R
WE'LL DETERMINE THE ACTUAL ANNUAL SIMPLE INTEREST RATE
THAT'S BEING PAID.
WELL, 1,920 x 1/3 = 640.
SO WE HAVE 80 = 640 R.
DIVIDE BOTH SIDES BY 640, SO WE HAVE R = THIS QUOTIENT.
SO WE'LL GO BACK TO THE CALCULATOR,
80 DIVIDED BY 640 = 0.125.
THIS IS THE DECIMAL VALUE OF THE ANNUAL INTEREST RATE.
MULTIPLYING BY 100 WE'LL CONVERT THIS TO A PERCENTAGE.
SO THE ACTUAL ANNUAL SIMPLE INTEREST RATE
PAID FOR THIS DISCOUNTED LOAN IS 12.5%.
OKAY. THAT'S GOING TO DO IT FOR THIS EXAMPLE.
I HOPE YOU FOUND THIS HELPFUL.