Mortgage Loan?

Question

The Young family is purchasing a $130,000 house with a VA mortgage. The bank is offering them a 25-year mortgage with an interest rate of 9.5%. They have $20,000 invested that could be used for a down payment. Since they do not need a down payment, Mr. Young wants to keep the money invested. Mrs. Young believes that they should make a down payment of $20,000. a) Determine the total cost of the house with no down payment & b) total cost, if they make a down payment of $20,000. c)Mr. Young believes that the $20,000 investment will have an annual rate of return of 10% compounded quarterly. Assuming that Mr. Young is right, calculate the value of the investment in 25 years. d) If the Young’s use the $20,000 as a down payment, their monthly payments will decrease. Determine the difference of the monthly payments in parts (a) and (b).

Answer 1

Nice practical problem. Great for an exam in a
math class!
Let's do each part separately:
a). This is an example of a present value problem.
We want to calculate the monthly payment, then
multiply the result by 300 to determine the total cost
of the house.
The formula for the present value of the loan is
P = R/i[1 -(1+i)^-n]
Here P is the value of the debt
or 130000
R is the monthly payment, the unknown
i is the interest rate or .095/12, since
the payments will be made monthly.
So i = .00791666.
n is the number of payment periods or 25*12 = 300.
Substituting and solving,
we find
R = 130000*.00791666/( 1-(1.00791666)^-300)
R = 1135.80
Total cost of house 1135.80*300 = 340741.48,
assuming 300 equal payments of 1135.80 are made.

b). Same calculation, except use 110000
instead of 130000 and we find
R = 961.19 and total cost of house = 288356.37

c). Here S = P(1+i)^n
and we have i = .10/4 = .025 and n = 100
So S = 20000(1.025)^100 = 236274.33

d). Difference = 1135.80 - 961.19 = 174.61.
Hope that helps!

Answer 2

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RE :Mortgage Loan?
The Young family is purchasing a $130,000 house with a VA mortgage. The bank is offering them a 25-year mortgage with an interest rate of 9.5%. They have $20,000 invested that could be used for a down payment. Since they do not need a down payment, Mr. Young wants to keep the money invested. Mrs. Young believes that they should make a down payment of $20,000. a) Determine the total cost of the house with no down payment & b) total cost, if they make a down payment of $20,000. c)Mr. Young believes that the $20,000 investment will have an annual rate of return of 10% compounded quarterly. Assuming that Mr. Young is right, calculate the value of the investment in 25 years. d) If the Young’s use the $20,000 as a down payment, their monthly payments will decrease. Determine the difference of the monthly payments in parts (a) and (b).
1 following 4 answers

Answer 3

a) 142350 = 130000 * 1.095

b) 130000-20000 = 110000 * 1.095 = 120450

c) I think I did something wrong, because I got a number that didn't make sence....

d) 142350/300 = 474.5 120450/300 = 401.5
diff = 73

Hope that helps

Answer 4

Michael Moore and Mike Hopkins asked the same question. You should read the answers side by side.

Answer 5

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