John just purchased a brand new car for $30,000. He paid $5,000 down payment and financed the rest at 5% compounded continuously over a period of 5 years with 2% fees on the balance. What is John's monthly payment? And what is the effective annual interest rate that John will pay on the loan? Finally, how much interest will John pay in 5 years? Any help will be appreciated and thanks.
$30,000 - $5,000 =$25,000 This the loan that John got.
5% comp. continuously is equivalent to=5.01% compounded monthly
John's monthly payment will be =$471.90 for 5 years or 60 months.
John will pay a fee of 2% on $25,000 or $500, which will deducted from $25,000.
$25,000 - $500 =$24,500 This is what John will actually get. So, based on above monthly payment of $471.90 and $24,500 over 60 months, his actual rate of interest comes to:
5.85% compounded monthly, or =6.01% effective annual rate.
Total interest that John will pay=$471.90 x 60 -$24,500=$3,814.02.
So, John's car will have cost him:$30,000 + $500 + $3,814.02=$34,314.02 over 5 years.
