Question 1173104: Michael Sanchez purchased a condominium for $73,000. He made a 20% down payment and financed the balance with a 30 year, 5% fixed-rate mortgage. (Round your answers to the nearest cent.
What is the amount (in $) of the monthly principal and interest portion, PI, of Michael's loan?
I was able to get the monthly payment of 392.01 and a down payment of 14,600. Not sure what the next step is.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! price of the condo was 73,000.
20% down was 73,000 * .2 = 14,600.
amount to be financed was 73,000 - 14,600 = 58,400.
30 year loan at 5% per year nominal results in:
360 month loan at (5/12)% per month.
financial calculator says that the payment at the end of each month needs to be 313.50.
not sure where you got 392.01 from, but that's not correct.
a payment of 392.01 for 360 months at 5% per year compounded monthly is for a loan of 73,024.
looks like you financed the whole thing rather than the net balance after paying the down payment.
my calculations indicate the payment at the end of each month needs to be 313.50.
it's actually 313.5038278 rounded to 2 decimal places.
the amount in dollars of the monthly payment that is principal and interest varies throughout the loan.
at the start of the loan the interest is a much higher percentage of the payment.
at the end of the loan, the principal is a much higher percentage of the payment.
you cannot come up with a fixed percentage of each monthly payment.
you can, however, come up with an average based on the total payments.
the monthly payment are 313.50 rounded to the nearest penny.
the total payments are 360 * 313.50 = 112,860
total principal paid is 58,400
total payments made is 112,860.
total interest paid is 112,860 minus 58,400 = 54,460.
average amount of equity in each payment would be equal to 58,400/112,860 = 51.75% rounded to 2 decimal places.
average amount of interest in each payment would be equal to 54,460/112,860 = 48.25% rounded to 2 decimal places.
as stated before, the actual amount of equity in each payment increases as the loan matures.
the following excerpts from an excel analysis show this to be true.
from this excel printout, the interest portion of the payment starts off as 77.6% of the current payment and 77.6% of the cumulative sum of the current payments.
the interest portion of the payments ends up as .41% of the current payment and 48.26% of the cumulative sum of the current payments.
my calculations showed 48.25% and the excel showed 48.26%.
the difference is in rounding.
i used the payment that was rounded to 2 decimal places.
excel used the more detailed payment which was probably rounded to a whole lot more decimal places.
the point of the excel presentation is that the percent of the payment that is equity and interest changes as the loan progresses through its life cycle.
if you want a fixed percentage, then it has to be an average from the sum of all payments
i'll be available to answer any questions you might have about this.
theo
|
|
|
