A man bought a house for $65000 and made a down payment of $30000. The balance is amortized by equal monthly od $100 each at 6% compounded monthly. By constructing a partial amortization schedule. What will be the outstanding principal and the Mans equity after the sixth payment
To calculate the outstanding principal and the man's equity after the sixth payment, we need to construct a partial amortization schedule. Since we know the down payment, the total price of the house, the monthly payment amount, as well as the interest rate, we can proceed with the calculation.
First, let's calculate the initial loan amount:
Loan amount = House price - Down payment = $65,000 - $30,000 = $35,000
Now, let's calculate the monthly interest rate:
Monthly interest rate = Annual interest rate / 12 months = 6% / 12 = 0.5% or 0.005 in decimals
The monthly payment is $100.
Using the above information, we can now set up the amortization table for the first six payments. Each payment will cover the interest for the month and the remaining part of the payment will go towards reducing the principal.
For each month, we will calculate the interest and the principal portion of the $100 payment as follows:
Interest for month = Outstanding principal * monthly interest rate
Principal portion of payment = Total monthly payment - interest for month
New outstanding principal = Previous outstanding principal - principal portion of payment
Calculating by month:
1. Month 1:
Interest = $35,000 * 0.005 = $175
Principal portion = $100 - $175 = -$75 (Negative value indicates a shortfall)
New outstanding principal = $35,000 + $75 (since this is an additional amount due to shortfall) = $35,075
2. Month 2:
Interest = $35,075 * 0.005 = $175.375
Principal portion = $100 - $175.375 = -$75.375
New outstanding principal = $35,075 + $75.375 = $35,150.375
We can already see the payments are not covering the interest; thus, the loan balance is increasing. This means that the payment of $100 is not enough to amortize the loan. In real life, the monthly payment would have to be higher to amortize the loan properly.
Given that the man's equity is the difference between the home's value and the outstanding loan balance, since the monthly payment isn't sufficient to reduce the loan's principal and instead it's increasing, his equity is reducing from the initial down payment value according to how much the loan balance increases.
However, since the loan is not being amortized with these monthly payments but is instead negatively amortizing, we cannot calculate the correct outstanding principal and equity after the sixth payment with the given values.
For the buyer to actually begin paying off the loan, his monthly payment needs to exceed the interest accrued each month. In this scenario, if he continues to pay only $100 per month, he will never pay off the house and his debt will continue to grow. To correct this, we would need to find a monthly payment that would sufficiently cover the interest and reduce the principal to eventually pay off the loan balance.