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.
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.