Question

You have just taken out a $22000 car loan with a 7% APR, compounded monthly. The loan is for 5 years.When you first make your payment in one month, how much of the payment will go toward the principal of the loan and how much will go towards the interest.

Answer 1

Solution:

The formula for calculating monthly payment given an APR of 7 % is

P = A * (r/12 ) / [ 1 – ( 1/ ( 1 + (r/12) ) n ) ]

Where r = APR   ; A = Principal loan amount ; n= No. of months

As per the information give in the question we have

APR = r = 7 % = 0.07

Thus Monthly discount rate = r/ 12 = 0.07 / 12 = 0.005833

A = $ 22,000 ;   n = 60 months ;

Applying the above information in the formula we have :

= 22,000 * (0.07/12 ) / [ 1 – ( 1/ ( 1 + (0.07/12) ) 60 ) ]

= 22,000 * (0.005833 ) / [ 1 – ( 1/ ( 1 + (0.005833) ) 60 ) ]

= 22,000 * (0.005833 ) / [ 1 – ( 1/ ( 1.005833) 60 ) ]

= 128.333333 / [ 1 – ( 1/ ( 1.005833) 60 ) ]

= 128.333333 / [ 1 – ( 1/ 1.417625 ) ]

= 128.333333 / [ 1 – 0.705405 ]

= 128.333333 / 0.294595

= 435.626368

Thus the monthly loan repayment will be = $ 435.626368

= $ 435.6264 ( If rounded off to four decimal places )

= $ 435.63 ( If rounded off to two decimal places )

Calculation of First month Interest payment :

The first month interest payment is = Principal amount of loan outstanding at the first month * Monthly Interest rate

= $ 22,000 * 0.005833

= $ 128.333333

Thus the First month Interest payment = $ 128.333333

= $ 128.3333 ( If rounded off to four decimal places )

= $ 128.33 ( If rounded off to two decimal places )

Calculation of amount of monthly payment that will go toward the principal of the loan :

The amount of monthly payment that will go toward the principal of the loan = Monthly loan repayment - The first month interest payment

= $ 435.626368 - $ 128.333333

= $ 307.293035

Thus the amount of monthly payment that will go toward the principal of the loan = $ 307.293035

= $ 307.2930 ( If rounded off to four decimal places )

= $ 307.29 ( If rounded off to two decimal places )

Note : Note : The value of ( 1.005833 ) 60   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.005833,60) = 1.417625