Question

In: Finance

A local finance company quotes an interest rate of 18 percent on one-year loans. So, if...

A local finance company quotes an interest rate of 18 percent on one-year loans. So, if you borrow $35,000, the interest for the year will be $6,300. Because you must repay a total of $41,300 in one year, the finance company requires you to pay $41,300/12, or $3,441.67, per month over the next 12 months.

a. what rate would legally have to be quoted?

b. what is the effective annual rate?

Solutions

Expert Solution

(a)  
Amount of loan (P)=   35000
  
Total months (n)=   12
Equal monthly Payment=   $3,441.67


Equal payments formula = P* i *((1+i)^n)/(((1+i)^n)-1)  
3441.67 = 35000*i*((1+i)^12)/(((1+i)^12)-1)  


We will Assume ínterest rate per month is 3%  
Equal Payment=
35000*0.03*((1+0.03)^12)/(((1+0.03)^12)-1)  
=3516.172992  
  
We will Assume ínterest rate per month is 2.5%

Equal Payment=
35000*0.025*((1+0.025)^12)/(((1+0.025)^12)-1)  
=3412.049445  


We will calculate (i) by interpolation formula  
interpolation formula = uper rate + (uper rate - lower rate)*(Uper amount - actual Payment)/(uper amount - lower amount)  
=0.03 - ((0.03-0.025)*(3516.172992-3441.67)/(3516.172992-3412.049445)
=0.003- 0.003577624569
=0.02642237543   or 2.642237543%
Per month rate is 2.642237543%  


So annual Rate legally have to be Quoted is 2.642237543%*12=   31.71%


(b)  
Effective annual rate =((1+monthly rate)^(no of months in a year))-1  
((1+   0.02642237543
0.3674559024   or 36.75%
  
So EAR of Loan is 36.75%   
  

Please thumbs up
  


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