Question

You have just taken out a $24,000 car loan with a 7% 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?

Answer 1

If the loan amount is P, rate on interest (monthly is r, and loan term is n the EMI will be

EMI= P*r[(1 +r)^n]/ [(1+ r)^n- 1]

= 24000*0.0058333[(1 +0.0058333)^60]/ [(1+ 0.0058333)^60- 1]

= 139.9992[(1.0058333)^60]/ [(1.0058333)^60- 1]

= 139.9992[1.4176224408]/ [1.4176224408- 1]

= 139.9992[1.4176224408]/ [0.4176224408]

= 139.9992[3.39450734037279]

= 475.23

Monthly EMI is 475.23

Interest part in first EMI = 24000* 0.0058333 = 139.99 or 140

Principle = 475.23 – 140 = 335.23

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