Question

You want to buy a house that costs $100,000. You have $10,000 for a down payment, but your credit is such that mortgage companies will not lend you the required $90,000. However, the realtor persuades the seller to take a $90,000 mortgage (called a seller take-back mortgage) at a rate of 9%, provided the loan is paid off in full in 3 years. You expect to inherit $100,000 in 3 years; but right now all you have is $10,000, and you can afford to make payments of no more than $9,000 per year given your salary. (The loan would call for monthly payments, but assume end-of-year annual payments to simplify things.) If the loan amortized over 3 years, how large would each annual payment be? Round your answer to the nearest cent. $ Could you afford those payments? If the loan were amortized over 30 years, what would each payment be? Round your answer to the nearest cent. $ Could you afford those payments? To satisfy the seller, the 30-year mortgage loan would be written as a balloon note, which means that at the end of the third year, you would have to make the regular payment plus the remaining balance on the loan. What would the loan balance be at the end of Year 3? Round your answer to the nearest cent. $ What would the balloon payment be? Round your answer to the nearest cent. $ Please explain how to solve on a financial calculator.

Answer 1

House Price = $ 100000, Mortgage Amount = $ 90000, Interest Rate = 9 % and Tenure =30 years

Let the annual repayments be $ P

Therefore, 90000 = P x (1/0.09) x [1-{1/(1.09)^(3)}]

90000 = P x 2.5313

P = 90000 / 2.5313 = $ 35554.93

As the home buyer can afford a maximum annual repayment of only $ 9000, this arrnagement is unaffordable to the home buyer.

In case, the tenure of the loan is 30 years and assuming an annual repayment of $ M, we have:

90000 = M x (1/0.09) x [1-{1/(1.09)^(30)}]

90000 = M x 10.27635

M = 90000 / 10.27635 = $ 8760.272

As the home buyer's annual repayments of $ 8760.272 is lower than the maximum possible repayment this option is affordable to the home buyer.

In case the home buyer goes for a balloon repayment note with a 30-year tenure, then for the first three years, the annual repayments will be $ 8760.272, followed by repaying the end of Year 3 mortgage outstanding amount in one go.

Mortgage Outstanding at the end of Year 3 = Present Value of Remaining Annual Repayments = 8760.272 x (1/0.09) x [1-{1/(1.09)^(27)}] = $ 87835.57

As the home buyer is expected to inherit $ 100000 in three years he/she can afford this balloon repayment option.