In: Finance

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?

(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%

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