The area of the rectangular floor in Tamara's room is 95 square feet. The width of the room is 8 feet.
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If this is the case, then you know by the polynomial remainder theorem that 
is a factor of 
, so there is some polynomial 
such that
A) The payment on the loan will be 1071.54, so after 300 payments, you will have repaid $321,462.00
b) Fees deducted from the loan amount for reporting purposes are
• 1/2% origination fee ($725)
• 3/4 point ($1087.50)
• $550 mortgage insurance fee
for a total of $2362.50.
Thus the proceeds of the loan are $142,637.50 and the reportable APR is the interest rate corresponding to the above payment on this amount.
Reportable APR: about 7.688%
c) The "real" APR would include the effect of the additional fees on the loan proceeds. The escrow amount is not a loan cost, so is not included. These additional fees reduce the proceeds by
$360 +395 +663 +125 +75 = $1618
so the "real APR" is calculated on proceeds of $141,019.50.
Real APR: about 7.819%
d) Payments on a 10-year loan of $145,000 are $1721.18 per month. That payment amount on proceeds of $141,019.50 correspond to an interest rate of ...
Real APR with early payoff: about 8.137%
There are various ways the payoff can be early. This calculation assumes you decide from the start to make payments in the amount that will result in early payoff. You could also pay a "balloon" payment after 10 years. I have not seen a description of how this calculation is made. I've only seen wording that says the "real APR is different if the payoff is early."
____
Several caveats:
• the methods described in your text are the ones you should use for this
• the different value of the final payment has not been figured in any of these calculations
• Here, the fees are deducted from the nominal loan amount. In real life, you will often add the fees to the loan amount so the proceeds are the amount necessary to close the sale on the property. (In other words, you'd make the loan for 148,980.50 so the proceeds were 145,000.)
b) Fees deducted from the loan amount for reporting purposes are
• 1/2% origination fee ($725)
• 3/4 point ($1087.50)
• $550 mortgage insurance fee
for a total of $2362.50.
Thus the proceeds of the loan are $142,637.50 and the reportable APR is the interest rate corresponding to the above payment on this amount.
Reportable APR: about 7.688%
c) The "real" APR would include the effect of the additional fees on the loan proceeds. The escrow amount is not a loan cost, so is not included. These additional fees reduce the proceeds by
$360 +395 +663 +125 +75 = $1618
so the "real APR" is calculated on proceeds of $141,019.50.
Real APR: about 7.819%
d) Payments on a 10-year loan of $145,000 are $1721.18 per month. That payment amount on proceeds of $141,019.50 correspond to an interest rate of ...
Real APR with early payoff: about 8.137%
There are various ways the payoff can be early. This calculation assumes you decide from the start to make payments in the amount that will result in early payoff. You could also pay a "balloon" payment after 10 years. I have not seen a description of how this calculation is made. I've only seen wording that says the "real APR is different if the payoff is early."
____
Several caveats:
• the methods described in your text are the ones you should use for this
• the different value of the final payment has not been figured in any of these calculations
• Here, the fees are deducted from the nominal loan amount. In real life, you will often add the fees to the loan amount so the proceeds are the amount necessary to close the sale on the property. (In other words, you'd make the loan for 148,980.50 so the proceeds were 145,000.)