Respuesta :
Solution:
Total amount that has to be paid after 30 years = $305,000 with a 30-year 5/1 ARM at 4.65% with a 1/12 cap structure.
As, amount will depreciate after each year.
Amount left after 6 years which is to be paid=
[tex]Amount = Principal \times [1-\frac{rate}{100}]^{time}\\\\A= 305,000\times [1-\frac{4.65}{100}]^{6}\\\\ A=305,000\times [\frac{95.35}{100}]^{6}\\\\ A=305,000\times [0.9535]^{6}\\\\ A=229204.966[/tex]
Amount Paid after 6 years = $ 305,000.00 - $ 229204.966
=$ 75795.034
Amount left, after 5 years which is to be paid=
[tex]Amount = Principal \times [1-\frac{rate}{100}]^{time}\\\\A= 305,000\times [1-\frac{4.65}{100}]^{5}\\\\ A=305,000\times [\frac{95.35}{100}]^{5}\\\\ A=305,000\times [0.9535]^{5}\\\\ A=240382.76[/tex]
Amount paid after 5 years= $ 305,000.00 - $ 240382.76
=$ 64617.24
Total amount that has to be paid between 5 to 6 years= $ 75795.034 - $ 64617.24=$ 11177.794
Monthly payment=
[tex]\frac{11177.794}{12}\\\\ =931.48[/tex]
So, monthly payment at the beginning of year 6= $ 931.48
