– YOU HAVE $3,000

ON A CREDIT CARD THAT CHARGES A 17%

INTEREST RATE. IF YOU WANT TO PAY OFF THE

CREDIT CARD IN TWO YEARS, HOW MUCH WILL YOU NEED TO PAY

EACH MONTH? THIS ASSUMES YOU DON'T CHARGE

ANYTHING NEW TO THE CARD. SO TO SOLVE THIS PROBLEM

WE'LL USE THE LOAN FORMULA GIVEN HERE BELOW. LET'S REVIEW

WHAT THE VARIABLES REPRESENT. P SUB ZERO IS THE STARTING LOAN

AMOUNT. D IS THE PAYMENT AMOUNT, OR, IN

THIS CASE, THE MONTHLY PAYMENT. R IS THE ANNUAL INTEREST RATE

EXPRESSED AS A DECIMAL. K IS THE NUMBER OF COMPOUNDS

PER YEAR. SINCE WE'RE PAYING MONTHLY WE'LL ASSUME THE INTEREST

IS COMPOUNDED MONTHLY. AND N IS THE NUMBER OF YEARS. SO FROM THE GIVEN INFORMATION

P SUB 0 = $3,000. THE CREDIT CARD CHARGES

17% INTEREST, SO R = 17% WHICH AS A DECIMAL

WOULD BE 0.17. YOU WANT TO PAY OFF

THE CREDIT CARD IN TWO YEARS, SO N = 2 YEARS. AND, AGAIN, YOU'RE MAKING

MONTHLY PAYMENTS, SO K = 12. AND WE'RE TRYING TO FIND

THE MONTHLY PAYMENT WHICH WOULD BE D. SO TO SET OUR EQUATION UP

WE WOULD HAVE 3,000 = THIS FRACTION HERE ON THE RIGHT. WE'RE LOOKING AT THE NUMERATOR, YOU WOULD HAVE E

x THE QUANTITY 1 MINUS THE QUANTITY + R

DIVIDED BY K, WHICH IS 0.17 DIVIDED BY 12

RAISED TO THE -2 x 12 POWER.

THIS IS ALL DIVIDED

BY THE FRACTION R/K OR 0.17 DIVIDED BY 12. WHEN SOLVING THIS FOR D WE DO HAVE TO BE CAREFUL

ABOUT ROUNDING. FOR EXAMPLE,

IF WE ROUND THIS SUM, THEN RAISE IT TO THIS POWER, AND THEN SOLVE FOR D WE'LL HAVE

MORE OF A ROUNDING ERROR THAN IF WE LEAVE THIS

IN THE EXACT FORM AND ROUND AT THE VERY END. LET'S TRY TO LEAVE THIS IN THE

EXACT FORM AND SOLVE FOR D. LET'S BEGIN BY CLEARING

THIS FRACTION HERE BY MULTIPLYING BOTH SIDES OF THE

EQUATION BY 0.17 DIVIDED BY 12.

IF IT'S HELPFUL, WE CAN THINK OF

THIS AS BEING OVER 1, THEREFORE THIS SIMPLIFIES TO 1. SO WE HAVE 3,000 X 0.17/12 = ON THE RIGHT WE HAVE D

X THE QUANTITY 1 MINUS THE QUANTITY 1 + 0.17

DIVIDED BY 12 RAISED TO THE POWER -24. AND NOW TO SOLVE FOR D WE'LL DIVIDE BOTH SIDES

BY THIS QUANTITY HERE. SO WE'LL DIVIDE BOTH SIDES BY

1 – THE QUANTITY 1 + 0.17 DIVIDED BY 12

RAISED TO THE POWER -24. NOTICE ON THE RIGHT SIDE

THIS SIMPLIFIES TO 1, SO WE HAVE D =

THIS QUOTIENT HERE WHICH WE'LL ROUND

TO THE NEAREST CENT. WHEN ENTERING THIS

INTO THE CALCULATOR WE WILL INCLUDE ANOTHER SET OF

PARENTHESIS FOR THE NUMERATOR. SO WE HAVE OPEN PARENTHESIS

(3,000 x 0.17 DIVIDED BY 12), CLOSE PARENTHESIS

FOR THE FRACTION, CLOSE PARENTHESIS

FOR THE NUMERATOR DIVIDED BY OPEN PARENTHESIS

FOR DENOMINATOR. AND THEN WE HAVE 1 – THE

QUANTITY 1 + 0.17 DIVIDED BY 12, CLOSE PARENTHESIS. THIS IS RAISED

TO THE -24TH POWER, AND CLOSE PARENTHESIS

FOR THE DENOMINATOR.

SO THE MONTHLY PAYMENT TO

NEAREST CENT WOULD BE $148.33. SO THIS IS THE MONTHLY PAYMENT

REQUIRED TO PAY OFF THIS CREDIT CARD

IN TWO YEARS. NOW LET'S GO BACK TO THE

CALCULATOR JUST FOR A MOMENT. THIS IS THE MONTHLY PAYMENT

WE WOULD MAKE EACH MONTH FOR TWO YEARS, WHICH MEANS YOU'D MAKE

24 PAYMENTS OVER THE TWO YEAR PERIOD. SO WE MULTIPLY THIS BY 24, THIS WOULD BE THE TOTAL AMOUNT

THAT YOU WOULD PAY OVER THE TWO YEAR PERIOD. NOTICE HOW SINCE THE CREDIT CARD

BALANCE WAS $3,000, NOTICE HOW YOU WOULD BE PAYING

ALMOST $560 IN INTEREST OVER THE TWO YEAR PERIOD. THIS IS BECAUSE THE INTEREST

RATE ON MOST CREDIT CARDS IS SO HIGH. NOTICE HOW THE INTEREST RATE

WAS 17%. I HOPE YOU FOUND THIS HELPFUL..

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