Question

You have just taken out a $ 30000 car loan with a 5 % ​APR, compounded monthly. The loan is for five years. When you make your first payment in one​ month, how much of the payment will go toward the principal of the loan and how much will go toward​ interest? (Note: Be careful not to round any intermediate steps less than six decimal​ places.)

I have tried it different ways but can't seem to figure it out, I think the problem I'm having is converting the 5% because the answer I get is $566.69 and it is wrong, the module says the correct answer is 441.14 can you show me step by step?

Answer 1

First Calculation of monthly installment (EMI)

We have

EMI = [P x I x (1+I)^N]/[(1+I)^N-1]

P =loan amount or Principal =30,000

I = Interest rate per month = 5%/12
[To calculate rate per month: if the interest rate per annum is 11%, the per month rate would be 11/(12 x 100)]

N = the number of installments = 5 years*12 =60

EMI = [30000 x 0.05/12 x (1+.05/12)^60]/[(1+0.05/12)^60-1]

= (125*1.28335867850351)/(1.28335867850351-1)

= 160.419834812939 / 0.28335867850351

= 566.137

In the first month, Out of the EMI of 566.137, 125 (30000*5%/12) will go towards interest and the balance 441.137 (441.14 Approx.) (566.137-125) will go towards principal.

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