Question

You purchase a home for $200,000 and borrow the entire amount from Broadway Bank at an APR of 6% with monthly payments. The maturity of your mortgage equals (30+X) years. a. (8 points) Draw a time line that depicts the cash flows from the mortgage payments i. compute the payment and show your inputs and work. ii. Use negative numbers for outflows and positive for inflows. b. (8 points) Compute the outstanding mortgage amount after you have made (10+Y) years of payments. i. Show this point on the time line, and ii. give the inputs to your computations for full credit. (8 points) c. (9 payments) What is the interest and principal component of your mortgage payment on the next mortgage payment made after (10+Y) years in part (b)? Show your computations.

Answer 1

c c c c c c c c c c c

//-!-!-!-!-!-!-!- {...} -!-!-!-!-!-!-!-!//

F0 30+X

on F0 we receive the 200,000 dollars

then each month (!) we made the installment payment (c)

this continues for the entire life of the mortgage until we reach the year 30 + X at which the mortgage ends and no more payment is done.

The outstanding amount will be the 200,000 less the capitalize installment over 10 + Y years.

Notice as the payments are monthly we use a monthly rate.

`200,000 - C * ((1+0.06/12)^((10+Y)12)-1 )/(0.06/12)`

Outstanding after 10 + Y years

`200,000 - C * ((1+0.005)^((120+12Y)-1 )/(0.005)`

the interest component will be the outstanding balance times rate

`(200,000 - C * ((1+0.005)^(120+12Y)-1 )/(0.005)) * 0.005`

reduced expression:

`(1,000 - C * ((1+0.005)^(120+12Y)-1)`

and the amortization of the installment quota less interest:

`C - (1,000 - C * ((1+0.005)^(120+12Y)-1)`

`C^2 * ((1+0.005)^(120+12Y)-1) -1,000C`

Step-by-step explanation:

As we don't know the values for X and Y we have to use the main formulas and reduce them the most we can.

If we are given values for X and Y we place them in the formulas and solve.