# Ex: Determine a Monthly Payment Needed to Pay Off a Credit Card

0

SINCE WE ' RE PAYING MONTHLY WE ' LL ASSUME THE INTEREST. THE CREDIT CARD IN TWO YEARS, SO N= 2
YEARS. AND, AGAIN, YOU ' RE MAKING.
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. IF WE ROUND THIS SUM, THEN RAISE IT TO THIS POWER, AND THEN SOLVE FOR D WE ' LL HAVE.

Video Transcript:

ON A CREDIT CARD THAT CHARGES A 17%.
RATE OF INTEREST. , if YOU WANT TO PAY OFF THE.
.
CREDIT CARD IN TWO YEARS, HOW MUCH WILL YOU NEED TO PAY.
EVERY MONTH? THIS ASSUMES YOU DON'' T CHARGE. ANYTHING NEW TO THE CARD.
'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. EACH YEAR.
CONSIDERING THAT WE ' RE PAYING MONTHLY WE ' LL ASSUME THE INTEREST. IS COMPOUNDED MONTHLY. AND N IS THE NUMBER OF YEARS
. 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. TO SET OUR EQUATION UP. WE'WOULD HAVE 3,000 =THIS FRACTION HERE ON THE.
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 BEWARE. ABOUT ROUNDING. FOR INSTANCE,. 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. SPECIFIC 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. WE HAVE 3,000 X 0.17/ 12 = ON THE RIGHT WE HAVE D.
X THE QUANTITY AMOUNT MINUS THE QUANTITY AMOUNT + 0.17.
DIVIDED BY 12 RAISED TO THE POWER -24. BY THIS QUANTITY HERE.
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. 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 After That WE HAVE 1 – THE.
QUANTITY 1 + 0.17 DIVIDED BY 12, CLOSE PARENTHESIS. THIS IS RAISED.
TO THE -24 TH POWER, AND CLOSE PARENTHESIS.
FOR THE DENOMINATOR.SO THE MONTHLY PAYMENT TO.
NEAREST CENT WOULD BE \$148.33. 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.
PRACTICALLY \$560 IN INTEREST OVER THE TWO YEAR PERIOD. BECAUSE THE INTEREST, THIS IS.
RATE ON MOST CREDIT CARDS IS SO HIGH. NOTIFICATION HOW THE INTEREST RATE.