1. According to Homes.com, a Hoover, Alabama home is priced at $195, 000. If a person was to pay a 20% down payment of $39,000, they will only be required to pay $1,009 per month (745 for principal and interest, 68 for insurance and 195 for taxes). This is a 30 year fixed mortgage at a rate of 4%.
a. How much interest will the purchaser of this home pay over the life of the loan, being that the loan is a 30 year fixed mortgage that will require the purchaser to pay $1009 per month? ($745 of this payment represents principal and interest, the rest of the amounts used to calculate payments include insurance and tax)
Solution: This problem requires the use of the Finance Charge formula:
The Finance charge is equivalent to the total of all monthly
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This mortgage is 30 years, and 30 years multiplied by 12 months is equivalent to 360. 360 multiplied by the monthly paymenst of $745 is equivalent to $268,200 or the total of all monthly payments.
The owner of this house paid a downpayment of 20% on the price ($195,000) fo the home, which is $39,000. $195,000 – 39,000 is equivalent to $156,000 or the amount financed.
The Finance Charge or Interest is equivalent to the Total of all monthly payments ($268,000) – The amount financed ($156,000) which is equivalent to $112,000.
b. What would the monthly payments on this home be as it relates to principal and interest alone, if the mortgage was a 25 year mortgage as opposed to being a 30 year mortgage? All other factors such as the 4% rate, the 20% down payment, etc. will remain the same. The total amount financed is $156,000.
Solution: This problem requies the use of the monthly payment formula. PMT is equivalent to present value times interest, all, divided by 1 minus the fraction of 1 divided by (1+i) raised to the number of payment periods.
PMT = Present value ($156,000) x Interest (4% / 12) or .33% or .0033. All divided by 1 – 1 divided by (1+.0033)^300 = $823.43
The monthly payments as it relates to principal and interst is