Maths-
General
Easy

Question

The Approximate annual interest rate r of a monthly installment loan is given by the formula:
r equals fraction numerator fraction numerator 24 left parenthesis n m minus p right parenthesis over denominator n end fraction over denominator open parentheses p plus fraction numerator n m over denominator 12 end fraction close parentheses end fraction
Where n is the total number of payments , m is the monthly payment and p is the amount financed.
a. Find the approximate annual interest rate for a four year signature loan $20,000 that has monthly payments of $500.

hintHint:

When we calculate annual interest rate we have to take the time period in months. Always remember to write the interest rate in percentage.
We are asked to calculate to annual interest rate for the given situations.

The correct answer is: Changing it to percent, we have: 0.09 × 100=9%


    Step 1:
    Here, the number of payments are for four years, that is, n = 4 × 12=48.
    The value of p = $20 and the monthly payment is, m = $500.
    Substituting the values in the equation, we have:
    r equals fraction numerator fraction numerator 24 left parenthesis n m minus p right parenthesis over denominator n end fraction over denominator open parentheses p plus fraction numerator n m over denominator 12 end fraction close parentheses end fraction
    equals fraction numerator fraction numerator 24 left parenthesis 48 space cross times space 500 minus 20 comma 000 right parenthesis over denominator 48 end fraction over denominator open parentheses 20 comma 000 space plus fraction numerator 48 space cross times space 500 over denominator 12 end fraction close parentheses end fraction
    equals fraction numerator fraction numerator 24 left parenthesis 24 comma 000 space minus space 20 comma 000 right parenthesis over denominator 48 end fraction over denominator left parenthesis 20 comma 000 space plus space 4 space cross times space 500 right parenthesis end fraction
    equals fraction numerator fraction numerator 4000 space cross times space 24 over denominator 48 end fraction over denominator 20 comma 000 space plus space 2 comma 000 end fraction
    equals fraction numerator 2000 over denominator 22 comma 000 end fraction
    = 0.09
    Thus, the interest , r = 0.09.
    Changing it to percent, we have: 0.09 × 100=9%

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