Question

A couple needs a mortgage of $300,000. Their mortgage broker presents them with two options: a 30-year mortgage at
8 1/2% interest or a 15-year mortgage at
7 3/4% interest. (Round your answers to the nearest cent.)

(a) Find the monthly payment on the 30-year mortgage and on the 15-year mortgage
30yr=
15yr=

Answer 1

I will do the first, you do the 2nd

i = .085/12 = .00708333..
n = 30(12) = 360
payment = p

PV = p(1 - (1+i)^-n)/i
300000 = p(1 - 1.00708333^-360)/.007083333)
300000 = p(130.0536..)
p= 2306.74

Answer 2

I got 2823.82 is this correct?

Answer 3

Find the total amount to be paid over the life of the 30-year mortgage and on the 15-year mortgage.
30-year $
15-year

I also tried doing the same method this way but it didn't work? can you show me how?

Answer 4

For your second, the 15-year plan

i = .0775/12 = .00645833..
n = 15(12) = 180

p( 1 - 1.00645833^-180)/.006458333 = 300000

I got p = 2823.83

you had the same, good job

As to your last question, you cannot just add up the payments.
e.g. a payment of $500 made today does not have the same value as that same payment of $500 made 10 years from now. Interest has to enter the picture.

Even though the common practise would be to simply multiply 2306.74 by 360 to get $830426.40 for the 30 year plan, and 2823.82 times 180 to get 508286.6 , these two sums do not tell a true picture about the "value".

Answer 5

Answer

Answer 6

100 to 2 extra