Question

You are going to buy a new car worth ​$24,400. The dealer computes your monthly payment to be ​$504.55 for 60 months of financing. What is the​ dealer's effective rate of return on this loan​ transaction?

The​ dealer's effective rate of return is ___​%. ​(Round to one decimal​ place.)

Answer 1

IN THE ABOVE IMAGE,

THE SOLUTION IS AS FOLLOWS :-

THE PRESENT VALUE OF A NEW CAR IS $24400 AND THE FINAL AMOUNT TO BE PAID AFTER 5 YEARS OR 60 MONTHS WHICH ALSO INCLUDES THE INTEREST AMOUNT IS $504.55 X 60 WHICH EQUALS $30273....THEREFORE, x IN THE IMAGE ABOVE TELLS THE MONTHLY EFFECTIVE RATE OF RETURN WHICH IS CALCULATED AS PRESENT VALUE PLUS TIMES INTEREST FOR 60 MONTHS AS (1 + x)^60 ...THE 1 IN THE BRACKET MEANS THE PRESENT VALUE , AS INTEREST IS PAID ON THE PRESENT VALUE ITSELF...THIS ALSO MEANS THAT THE FINAL AMOUNT IS THE PRESENT VALUE PLUS THE INTEREST ON PRESENT VALUE FOR 60 MONTHS...

FOR ANNUAL EFFECTIVE RATE OF RETURN INSTEAD OF MONTHLY EFFECTIVE RATE , THE ABOVE IMAGE TELLS , THAT THE FINALVALUE FROM PRESENT VALUE AND INTEREST ON PRESENT VALUE FOR 60 MONTHS SHOULD BE EQUAL TO THE FINAL VALUE FROM PRESENT VALUE AND INTEREST ON THE PRESENT VALUE FOR 5 YEARS....THEREFORE , i ABOVE TELLS THE ANNUAL EFFECTIVE RATE OF RETURN....ANNUAL EFFECTIVE RATE MEANS THAT THE INTEREST IS PAID AT THE END OF EACH YEAR THAT IS ANNUALLY AND MONTHLY RATE MEANS THAT THE INTEREST IS PAID AT THE END OF EACH MONTH...