Miss Crystal Palace just purchased – you guessed it – a crystal palace for $650,000. She makes a 25% down payment and finances the balance with a mortgage at an interest rate of 5.6% for 15 years, making monthly payments. a. What amount will she borrow? b. Complete the amortization table for the first three payments. (Show all work!)

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Miss Crystal Palace just purchased – you guessed it – a crystal palace for $650,000. She makes a 25% down payment and finances the balance with a mortgage at an interest rate of 5.6% for 15 years, making monthly payments. a. What amount will she borrow? b. Complete the amortization table for the first three payments. (Show all work!)

Mathematics
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  • phi
can you answer (a) ? 75% of 650,000 or 650,000- 25% of 650,000
162500?
oh wait no. 649999.75?

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no isn't my first answer right?
  • phi
If you put down a down-payment, do you expect it to be all 650,000? to do this, remember that 25% is the same as 25/100 (or 1/4)
is it 162500?
  • phi
that is the down payment. How much is the loan?
162500(1+0.056/12)^12*15 162500(1+0.056/12)^180 (162500)(2.311845392)=$375,674.88
that's what I did...
ohh in my equation where i put 162500.. is that supposed to be 487500 instead?
  • phi
162,500 is 1/4 of the 650,000 162,500 is the amount paid up front. You must now borrow the remainder. so your work up above looks good except 162500 is not the correct amount for the loan
the amount of the loan is 1,127,024.63?
  • phi
For (a), I think they want 487,500 to do (b) you have to figure out how much the total loan ends up costing. Is that the 1,127,024 number?
yes the total loan I calculated is 1,127,024.63 I believe.
  • phi
now find the monthly payment
how? what formula?
6261.25 a month?
  • phi
now you can do the amortization schedule start with the loan balance at the start 487500 add one month of interest (0.056/12)*487500 then subtract off the payment to get the loan balance for the next month. do the same thing for the 2nd (and 3rd) month, except use the new loan principal
what new loan principal?
  • phi
when you make a payment, the amount you owe goes down
(0.056/12)*487500= 2275
487500-2275= 485225 for the next month?
2264.38--485235.62 2264.43--482971.19
how do I put that in a chart though with the.. amount of payment interest payment applied to principal and balance?
  • phi
OK, I just checked about loans. there is a formula to figure out the monthly payment FV= payment *( (1+i)^n -1)/i where future value FV is the number you found, does this look familiar?
yeah, give me a sec.
so the formula I used gave me 9268.65 as the monthly payment
  • phi
how? I get something else
P=1127024.63 n=180 r/m=0.56/12=0.0046666667 1127024.63(1+0.0046666667)^180=R[(1+0.0046666667)^180-1)/(0.0046666667)] 2605506.713=R(281.1097278) R=9268.65
the amount is 1127024.63 the annual rate is 5.6% and the time is 15 years
and the interest payment is 5259.45
  • phi
I match up, but with 1127024.63=R(281.1097278)
4009.2 is the applied principal and the balance is 1127024.63
do I not solve 1127024.63(1+0.0046666667)^180 that?
because in this example I have is shows to do that..
  • phi
for your formula, it looks like you should use the original loan amount on the left hand side. Do you notice that the left side is future value (1,237,024) which can be calculated as 487500*(1+0.056/12)^180
ohh so after solving it becomes 1127024.63
so is the monthly payment 4009.20?
  • phi
yes. so now to the amort. to answer amount of payment interest payment applied to principal and balance? you have the first part. interest is principal* 0.0046666667 (5.6% /12) so you start with P (487500) add interest subtract payment get new P (call it P2 for second month) The interest payment is the amount of interest due. the applied to principal is the amount of the payment left over after paying the interest P2 is the balance
wait wait.. is the interest payment 5259.45? (1127024.63)(0.0046666667)(1)
  • phi
No, you use Present value (not future value) when you apply the interest.
(487500)(0.0046666667)(1)=2275.00
  • phi
that looks good. now the payment pays that interest and what is left over pays down the principal
4009.20-2275.00=1734.20?
  • phi
so now how much is the new principal?
485765.8?
  • phi
so put those numbers in the first row. now do it again with P=485765.80
so.. 1734.20*0.0046666667*1?
  • phi
You seem to be missing the main point. you pay interest on the dollars you owe (think of it as rent) after one payment you owe 485765.80. that is what the interest is on (not the 1734)
2266.91? that is the next interest payment for month 2?
  • phi
yes
then 1742.29 is the applied principal for month 2?
  • phi
yes
then the next balance is 484023.51?
  • phi
yes. one more payment to go
2258.78 for the interest payment?
and 1750.42 and the applied principal?
  • phi
yes
  • phi
Here is a site that computes the amort http://bretwhissel.net/cgi-bin/amortize
thank you so much for your help!
  • phi
It helped remind me how to do this stuff. It is a bit complicated.
haha yeah, well before I had absolute no idea where to start. Thank you so much for helping me..
Down payment= \[\frac{ 2.5 }{100}*650,000\] =633,750 was the amount borrowed.

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