Question

I just dont get this at all

Maria is debating between two different mortgages for $155,000. She found a 20-year fixed rate loan at 7.35% and 15-year fixed rate loan at the same rate. How much more interest will she pay for the 20-year loan versus the 15-year loan

$2,492.45

$40,013.40

$57,737.40

$5,158.30

Answer 1

first determine what the monthly payments will be for each loan.
use financial calculator or present value equation

Answer 2

thats what i keep trying to do i just dont understand what im doing wrong.

Answer 3

what math class is this for?

Answer 4

advanced algebra with financial apps

Answer 5

ok guess you need to do it by hand
here is present value equation which is a geometric sequence
i = monthly int rate
v = 1/(1+i)
20 yr loan (240 months)
\[155,000 = P(v + v^{2}+...v^{240})\]
15 yr loan (180 months)
\[155,000 = P(v + v^{2}+...v^{180})\]
use formula for sum of geometric series
\[S_n = v +v^{2}+...v^{n} = \frac{v(1-v^{n})}{1-v}\]
Now you can find the monthly payments for each loan
multiply the payment by length of loan to get total payment, subtract loan amount to get total interest paid

Answer 6

P is monthly payment

Answer 7

its b.

Answer 8

ok, are you asking or telling me...i haven't worked out the answer yet

Answer 9

yes its B
do you understand how to figure it out now?

Answer 10

yes thanks
i have another question tho.

Answer 11

Will is buying a house for $185,000. He is financing $165,000 and obtained a 30-year, fixed-rate mortgage with a 6.725% interest rate. How much are his monthly payments?

$506.25

$1,067.45

$1,196.83

$1,656.73

Answer 12

same thing as before...except number of months is 360
PV = 165,000
i = 6.725% /12
v = 1/(1+i)

\[165,000 = P(v+v^{2}+...v^{360})\]
solve for P using the Sum formula

Answer 13

Correct answer: $1,067.45