Annabelle bought 3 points on a 15-year, fixed-rate mortgage with a rate of 5.97%. If she had not purchased points, her interest rate would have been 6.72%. If Annabelle finances $227,650, how much money did she save over the life of the loan by purchasing points?

$9,975.30

$16,804.80

$14,528.30

$6,829.50

Question

Annabelle bought 3 points on a 15-year, fixed-rate mortgage with a rate of 5.97%. If she had not purchased points, her interest rate would have been 6.72%. If Annabelle finances $227,650, how much money did she save over the life of the loan by purchasing points?

 $9,975.30

 $16,804.80

 $14,528.30

 $6,829.50

phi · Answer

did you figure out the monthly payment, and then the total amount paid?
then subtract the original amount, and the remaining is the interest paid.

How far did you get ?

anonymous · Answer

only with the formula @phi

phi · Answer

what is the formula ?

anonymous · Answer

M=B[((i)(1+i)^(n*t))/((1+i)^(n*t)-(1))]

anonymous · Answer

B=227,650
t=15
n=12 
I dont know the rest

phi · Answer

for the first loan i= monthly interest rate.  yearly rate is 5.97% = 0.0597
divide by 12 to get  i
i =  0.0597/12

anonymous · Answer

i=0.004975

phi · Answer

fill in the variables and figure out the monthly payment

anonymous · Answer

http://www.wolframalpha.com/input/?i=M%3D227650%5B%28%280.004975%29%281%2B0.004975%29%5E%2812*15%29%29%2F%28%281%2B0.004975%29%5E%2812*15%29-%281%29%29%5D

phi · Answer

wolf makes it easy.
now total paid is 180 payments times monthly payment

anonymous · Answer

180 * 1917.35 ?

phi · Answer

yes
then subtract the principal  to get the interest paid
then add in the points (pre-paid interest)

anonymous · Answer

345123. - 227650 + 3 ?

phi · Answer

3 points means 3% of the original  so  0.03*$227,650

phi · Answer

and I would keep the cents

anonymous · Answer

68295 ?

phi · Answer

it looks like you misplaced a decimal point

anonymous · Answer

6829.50

anonymous · Answer

:O

anonymous · Answer

Thats the correct answer : ?

phi · Answer

no that is the amount the points cost.

the total interest on loan 1 is 
345123.42 - 227650 +6829.50

total paid -  original  + points

now you need to find the total interest paid on the 2nd loan
it will be more

then find the difference between the two loans

anonymous · Answer

http://www.wolframalpha.com/input/?i=345123.42%20-%20227650%20%2B6829.50&t=crmtb01&f=rc

phi · Answer

yes.  now do the same thing for the 2nd loan  ... but it won't have points

anonymous · Answer

add the other annual rate ?

phi · Answer

yes, change to the new rate   i = 0.0672/12
everything else is the same.  now find the payment, then multiply by 180 to get the amount paid

then subtract the original loan to get the interest paid

anonymous · Answer

then would I get my final answer ?

phi · Answer

did you get the interest paid on the 2nd loan ?

anonymous · Answer

i got 134277.8

phi · Answer

yes,  now find the difference between 134277.8 and 124302.92

that is the amount of interest saved

anonymous · Answer

how do I do that ?

phi · Answer

the difference between 2 numbers is found by subtracting one from the other

anonymous · Answer

I got 9974.88