Jacson purchased a house for Birr 50,000. He made an amount of down payment and pay monthly Birr 600 to retire the mortage for 20 years at annual interest rate of 24% compounded monthly.
Find mortage
down payment
interest charged
percentage of down payment to selling price.
Present worth of 600 monthly for 20 years at APR=24%:
P=A*(P/A, 2%, 480)
=600*(1.02^480-1)/[(.02)(1.02^480)]
=29,997.766
Therefore down-payment
=50000-P
=50000-29,997.766
=20,002.23
Interest charged
=future value - present value
=29997.766*[(1.02^480)-1]
=402,845.97
(no interest paid on down-payment).
I'll leave the calculation of percentage of down-payment to selling price to you.
P = (Po*r*t)/(1-(1+r)^-t.
P = 600 * 240 = 144,000
X = Down payment.
Po = 50,000-x
r = 0.24/12 = 0.02/mo.
t = 20 * 12 = 240 mo.
144,000 = (50,000-x)*0.02*240)/(1-(1.02)^(-240))
X = 20,258.87
Po = 50,000-20,258.87 = 29,741.13
I = P-Po
What about the mortgage?
To find various details related to the mortgage, we can follow these steps:
Step 1: Calculate the mortgage:
The mortgage can be calculated using the loan formula:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M - Mortgage amount
P - Purchase price
r - Monthly interest rate (annual interest rate / 12)
n - Total number of payments (20 years * 12 months/year)
Substituting the given values:
P = Birr 50,000
r = 24% / 12 = 0.02 (monthly interest rate)
n = 20 years * 12 months/year = 240 months
M = 50000 * (0.02 * (1 + 0.02)^240) / ((1 + 0.02)^240 - 1)
M ≈ Birr 1340.45
Therefore, the mortgage amount is approximately Birr 1340.45.
Step 2: Calculate the down payment:
We know that the down payment is the difference between the purchase price and the mortgage amount.
Down payment = Purchase price - Mortgage amount
Down payment = Birr 50000 - Birr 1340.45
Down payment ≈ Birr 48659.55
Therefore, the down payment is approximately Birr 48659.55.
Step 3: Calculate the interest charged:
To calculate the interest charged over the 20-year period, we can subtract the sum of all monthly payments from the total mortgage amount.
Total monthly payment = Monthly payment * Total number of payments
Total monthly payment = Birr 600 * 240
Total monthly payment = Birr 144,000
Interest charged = Total monthly payment - Mortgage amount
Interest charged = Birr 144,000 - Birr 1340.45
Interest charged ≈ Birr 142659.55
Therefore, the interest charged over the 20-year period is approximately Birr 142659.55.
Step 4: Calculate the percentage of down payment to selling price:
The percentage of the down payment to the selling price can be calculated using the formula:
Percentage = (Down payment / Purchase price) * 100
Percentage = (Birr 48659.55 / Birr 50000) * 100
Percentage ≈ 97.31%
Therefore, the percentage of the down payment to the selling price is approximately 97.31%.