Question

You have just purchased a car and, to fund the purchase, you borrowed $25,500. If your monthly payments are $360.24 for the next 7 years, what is the APR of the loan?

Answer 1

(a)      
Amount of loan (P)=   25500  
      
Total months in 7 years (n)=7*12=   84  
Equal monthly Payment=   $360.24  

Equal payments formula = P* i *((1+i)^n)/(((1+i)^n)-1)      
360.24 = 25500*i*((1+i)^84)/(((1+i)^84)-1)      
We will Assume ínterest rate per month is 0.5% or    0.005  
      
25500*0.005*((1+0.005)^84)/(((1+0.005)^84)-1)      
372.5181393      
      
We will Assume ínterest rate per month is 0.4% or    0.004  
25500*0.004*((1+0.004)^84)/(((1+0.004)^84)-1)      
358.0231432      

Actual Payment is in between two payments calculated by i. so We will calculate (i) by interpolation formula      

interpolation formula = uper rate - (uper rate - lower rate)*(Uper value - actual value)/(uper value - lower value)      
0.005 - ((0.005-0.004)*(372.5181393-360.24)/(372.5181393-358.0231432)      
0.005-   0.00084706  
0.00415294
Per month rate is 0.00415294      
So annual Rate APR of loan is 0.00415294*12=   0.04984   or 4.98%