Answer :
Answer:
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.
[tex]200,000 - C \times \frac{(1+0.06/12)^{(10+Y)12}-1 }{0.06/12}[/tex]
Outstanding after 10 + Y years
[tex]200,000 - C \times \frac{(1+0.005)^{(120+12Y}-1 }{0.005}[/tex]
the interest component will be the outstanding balance times rate
[tex](200,000 - C \times \frac{(1+0.005)^{120+12Y}-1 }{0.005}) \times 0.005[/tex]
reduced expression:
[tex](1,000 - C \times ((1+0.005)^{120+12Y}-1) [/tex]
and the amortization of the installment quota less interest:
[tex]C - (1,000 - C \times ((1+0.005)^{120+12Y}-1)[/tex]
[tex]C^2 \times ((1+0.005)^{120+12Y}-1) -1,000C[/tex]
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.