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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