Question

In: Finance

You have just taken out a $22000 car loan with a 7% APR, compounded monthly. The...

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.

Solutions

Expert Solution

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


Related Solutions

You have just taken out a $19,000 car loan with a 7% ​APR,compounded monthly. The...
You have just taken out a $19,000 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?  (Note: Be careful not to round any intermediate steps less than six decimal places.)
You have just taken out a $26,000 car loan with a 7 % APR, compounded monthly....
You have just taken out a $26,000 car loan with a 7 % APR, compounded monthly. The loan is for five years. When you make your first payment in one​ month, how much of the payment will go toward the principal of the loan and how much will go toward​ interest?  ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.) When you make your first​ payment,​$__ will go toward the principal of the loan and...
You have just taken out a $23000 car loan with a ​5% APR, compounded monthly. The...
You have just taken out a $23000 car loan with a ​5% APR, compounded monthly. The loan is for five years. When you make your first payment in one​ month, how much of the payment will go toward the principal of the loan and how much will go toward​ interest?  ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.) When you make your first​ payment, ​$___ will go toward the principal of the loan and...
You have just taken out a $29,000 car loan with a 4% ​APR, compounded monthly. The...
You have just taken out a $29,000 car loan with a 4% ​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.) When you make your first​ payment, __________ $ will go toward the principal of the loan...
You have just taken out a $15,000 car loan with a 6% APR, compounded monthly. The...
You have just taken out a $15,000 car loan with a 6% APR, compounded monthly. The loan is for five years. When you make your first payment in one​ month, how much of the payment will go toward the principal of the loan and how much will go toward​ interest?  ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.) When you make your first​ payment,​$___will go toward the principal of the loan and ​$___ will...
You have just taken out a $20,000 car loan with a 6% APR, compounded monthly. The...
You have just taken out a $20,000 car loan with a 6% 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?
You have just taken out an $18,000 car loan with a 6% ​APR, compounded monthly. The...
You have just taken out an $18,000 car loan with a 6% ​APR, compounded monthly. The loan is for five years. When you make your first payment in one​ month, how much of the payment will go toward the principal of the loan and how much will go toward​ interest? QUESTION When you make your first​ payment, ​$????? will go toward the principal of the loan and ​$???? will go toward the interest
(1)You have just taken out a $20 000 car loan with a 4% APR, compounded monthly....
(1)You have just taken out a $20 000 car loan with a 4% 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 to fewer than six decimal places.) 2)You have just sold your house for $ 1 100 000 in cash. Your...
You have just taken out a $ 30000 car loan with a 6 % ​APR, compounded...
You have just taken out a $ 30000 car loan with a 6 % ​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.) When you make your first​ payment, ​ $(blank)? will go toward the principal of...
Your firm has taken out a $ 455, 000 loan with 8.6 % APR​ (compounded monthly)...
Your firm has taken out a $ 455, 000 loan with 8.6 % APR​ (compounded monthly) for some commercial property. As is common in commercial real​ estate, the loan is a 5​-year loan based on a 15​-year amortization. This means that your loan payments will be calculated as if you will take 15 years to pay off the​ loan, but you actually must do so in 5 years. To do​ this, you will make 59 equal payments based on the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT