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=
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
I got 2823.82 is this correct?
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?
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
100 to 2 extra
To find the monthly payment for each mortgage option, we can use the formula for calculating the monthly mortgage payment:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
- M is the monthly payment
- P is the principal amount (mortgage amount)
- r is the monthly interest rate (annual interest rate divided by 12)
- n is the total number of payments (30 years = 360 months for the 30-year mortgage, and 15 years = 180 months for the 15-year mortgage)
First, let's calculate the monthly payment for the 30-year mortgage:
Principal amount (P) = $300,000
Annual interest rate = 8 1/2% = 8.5%
Monthly interest rate (r) = 8.5% / 12 = 0.7083%
Total number of payments (n) = 30 years * 12 months = 360 months
r = 0.7083 / 100 = 0.007083 (decimal)
M = 300000 * (0.007083 * (1 + 0.007083)^360) / ((1 + 0.007083)^360 - 1)
Using a calculator, we can evaluate this expression to find the monthly payment for the 30-year mortgage.
Now, let's calculate the monthly payment for the 15-year mortgage:
Principal amount (P) = $300,000
Annual interest rate = 7 3/4% = 7.75%
Monthly interest rate (r) = 7.75% / 12 = 0.6458%
Total number of payments (n) = 15 years * 12 months = 180 months
r = 0.6458 / 100 = 0.006458 (decimal)
M = 300000 * (0.006458 * (1 + 0.006458)^180) / ((1 + 0.006458)^180 - 1)
Using a calculator, we can evaluate this expression to find the monthly payment for the 15-year mortgage.