Question

# You have taken out a \$22.000 car loan with a 7% APR, compounded monthly. The loan...

You have taken out a \$22.000 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 towards the principal of the loan and how much will go towards the interest?

First we need to find out the EMI that will be paid on monthly basis

So Given data -

Loan amount (L) = \$22000

Tenure (n) = 5 * 12 = 60 Months

Monthly Interest rate ( i) = 7% /12 = 0.5833 % = 0.005833

Now

EMi = ( L * i) * {( 1 +i)n / (1+ i)n - 1)

put the values

EMI = ( 22000* 0.005833) * { ( 1+0.005833)60 / ( 1+0.005833)60 - 1}

= 128.326 * { 1.4175 / (1.4175 - 1)}

= 128.326 * (1.4175 / 0.4175)

EMI   = \$ 435.693

Now lets find out th principal and interest part in First month's payment

EMI = Interest + principal

\$ 435.693 = (22000 * 0.5833%) + Principal

435.693 = 128.326 + Principal

435.693 - 128.326 = Principal

\$307.367 = Principal

Therefore in first month's payment

Interest = (22000 * 0.5833%) = \$128.326

Principal = \$307.367

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