Question

15. You have just purchased a car and taken out a $50,000 loan. The loan has a 5-year term with monthly payments and an APR of 6%. How much will you pay in interest, and how much will you pay in principal, during the first month and second month

Answer 1

Answer:

find answers below

Explanation:

First and foremost, we need to determine the payment on a monthly basis in order to proceed further as shown thus:

PV(loan amount)=monthly payment*(1-(1+r)^-n/r

loan amount=$50,000

the monthly payment is the unknown

r=monthly interest rate=6%/12=0.5%

n=number of monthly payments in 5 years=5*12=60

50,000=monthly payment*(1-(1+0.5%)^-60/0.5%

50,000=monthly payment*(1-(1.005 )^-60/0.005

50,000=monthly payment*(1-0.74137220 )/0.005

50,000=monthly payment*0.25862780 /0.005

monthly payment=50,000*0.005/0.25862780 =$966.64  

first month:

amount paid $966.64  

interest=0.5 %*$50,000=$250

principal paid=monthly payment-interest=$966.64-$250=$716.64

loan balance=$50,000-$716.64=$49,283.36  

second month:

amount paid $966.64  

interest =0.5%*$49,283.36=$246.42  

principal paid=$966.64-$246.42 =$720.22