Mathematics
Grade10
Easy

Question

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

  1. 9 %
  2. 10 %
  3. 8 %
  4. 5 %

Hint:

The Simple Interest (S.I.) formula is a way to figure out how much interest will accrue on a given principal sum of money. The interest charged on a loan or deposit is known as compound interest. Here we have given an expression straight r space equals space fraction numerator open square brackets fraction numerator 24 space left parenthesis nm space minus space straight p right parenthesis over denominator straight n end fraction close square brackets over denominator open parentheses straight p space plus space nm over 12 close parentheses end fraction, we have to find find the approximate annual interest rate (to the nearest tenth percent) for a four-year.

The correct answer is: 9 %


    So now we know that the cost you pay annually for borrowing money, including fees, is stated as a percentage and is known as the annual percentage rate (APR).
    We have given the expression as: 
    straight r space equals space fraction numerator open square brackets fraction numerator 24 space left parenthesis nm space minus space straight p right parenthesis over denominator straight n end fraction close square brackets over denominator open parentheses straight p space plus space nm over 12 close parentheses end fraction
H e r e colon
p equals $ 20 comma 000 semicolon space
m equals $ 500 comma space
n equals 4 cross times 12 equals 48 space m o n t h s
N o w space l e t s space c o n s i d e r space t h e space g i v e n space e x p r e s s i o n space w i t h space 100 percent sign comma space w e space g e t colon colon
straight r space equals space fraction numerator open square brackets fraction numerator 24 space left parenthesis nm space minus space straight p right parenthesis over denominator straight n end fraction close square brackets over denominator open parentheses straight p space plus space nm over 12 close parentheses end fraction
P u t t i n g space t h e space v a l u e s space i n space i t comma space w e space g e t colon
r space equals space fraction numerator open square brackets begin display style fraction numerator 24 space left parenthesis left parenthesis 48 cross times 500 right parenthesis – 20000 right parenthesis over denominator 60 end fraction end style close square brackets space space over denominator open square brackets 20000 plus begin display style fraction numerator left parenthesis 48 space cross times space 500 right parenthesis over denominator 12 end fraction end style close square brackets space end fraction space
r space equals space fraction numerator open square brackets begin display style fraction numerator 24 space left parenthesis 24000 – 20000 right parenthesis over denominator 60 end fraction end style close square brackets space space over denominator open square brackets 20000 plus begin display style fraction numerator left parenthesis 24000 right parenthesis over denominator 12 end fraction end style close square brackets space end fraction
r space equals space fraction numerator open square brackets begin display style fraction numerator 24 space left parenthesis 4000 right parenthesis over denominator 60 end fraction end style close square brackets space space over denominator open square brackets begin display style fraction numerator 240000 plus 24000 over denominator 12 end fraction end style close square brackets space end fraction
r space equals space fraction numerator open square brackets begin display style 96000 over 5 end style close square brackets space space over denominator open square brackets begin display style 264000 over 1 end style close square brackets space end fraction
r space equals space 19200 over 264000
r equals 0.072 cross times 100 equals 7.2 percent sign

    Here we sed the concept of simple interest, compound interest and found out the annual rate. Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. So the annual rate percent is 7.2%.

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