Question
Ato Assefa purchased a house for Br. 115, 000. He made a 20% down payment with the
balance amortized by a 30 year mortgage at an annual interest of 12% compounded monthly
so as to amortize/ retire the debt at the end of the 30
th
year.
balance amortized by a 30 year mortgage at an annual interest of 12% compounded monthly
so as to amortize/ retire the debt at the end of the 30
th
year.
Answers
GPT 3.5
The down payment made by Ato Assefa is 20% of Br. 115,000, which is 0.20 x 115,000 = Br. 23,000.
The amount financed through the mortgage is the remaining balance after the down payment, which is Br. 115,000 - Br. 23,000 = Br. 92,000.
To calculate the monthly payment, we can use the formula for the monthly payment on a mortgage:
M = P[r(1 + r)^n]/[(1 + r)^n - 1],
where M is the monthly payment, P is the principal amount (Br. 92,000), r is the monthly interest rate (12% annual rate divided by 12 months = 1% or 0.01 monthly rate), and n is the total number of payments (30 years x 12 months = 360 payments).
Plugging in the values, we get:
M = 92000[0.01(1 + 0.01)^360]/[(1 + 0.01)^360 - 1].
Calculating this result gives us the monthly payment that Ato Assefa needs to make to retire the debt at the end of the 30th year.
The amount financed through the mortgage is the remaining balance after the down payment, which is Br. 115,000 - Br. 23,000 = Br. 92,000.
To calculate the monthly payment, we can use the formula for the monthly payment on a mortgage:
M = P[r(1 + r)^n]/[(1 + r)^n - 1],
where M is the monthly payment, P is the principal amount (Br. 92,000), r is the monthly interest rate (12% annual rate divided by 12 months = 1% or 0.01 monthly rate), and n is the total number of payments (30 years x 12 months = 360 payments).
Plugging in the values, we get:
M = 92000[0.01(1 + 0.01)^360]/[(1 + 0.01)^360 - 1].
Calculating this result gives us the monthly payment that Ato Assefa needs to make to retire the debt at the end of the 30th year.