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
i**nterest** and the balance **441.137 (441.14
Approx.)** **(566.137-125)** will go towards
**principal.**

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