Ato Liku purchases a house for Br. 250, 000. He makes a 20% down payment, with a
balance amortized by a 30 year mortgage at an annual interest rate of 12% compounded
monthly.
a) Determine the amount of the monthly mortgage payment.
b) What is the total amount of interest Ato Liku will pay over the life of the
mortgage?
c) Determine the amount of the mortgage Ato Liku will have paid after 10
years?
a) To determine the monthly mortgage payment, we first need to calculate the principal amount of the mortgage. Ato Liku made a 20% down payment, so the principal amount is 80% of Br. 250,000, which is Br. 200,000.
The annual interest rate is 12%, compounded monthly. So the monthly interest rate is 12%/12 = 1% or 0.01.
The number of monthly payments over 30 years is 30*12 = 360 months.
Using the formula for monthly mortgage payment:
M = P[r(1+r)^n]/[(1+r)^n - 1]
where M is the monthly mortgage payment, P is the principal amount (Br. 200,000), r is the monthly interest rate (0.01), and n is the number of monthly payments (360).
M = 200,000[0.01(1+0.01)^360]/[(1+0.01)^360 - 1]
M ≈ Br. 1,899.27
So, the monthly mortgage payment is Br. 1,899.27.
b) To calculate the total amount of interest paid over the life of the mortgage, we can multiply the monthly payment by the total number of payments and then subtract the principal amount.
Total amount of interest = (1,899.27 * 360) - 200,000
Total amount of interest ≈ Br. 323,737.20
So, Ato Liku will pay approximately Br. 323,737.20 in interest over the life of the mortgage.
c) To determine the amount of the mortgage Ato Liku will have paid after 10 years, we need to calculate the total number of payments after 10 years, which is 10 x 12 = 120 payments.
Mortgage paid after 10 years = 1,899.27 * 120 = Br. 227,912.40
So, after 10 years, Ato Liku will have paid approximately Br. 227,912.40 towards the mortgage.