Question

You want to buy a house that costs $210,000. You have $21,000 for a down payment, but your credit is such that mortgage companies will not lend you the required $189,000. However, the realtor persuades the seller to take a $189,000 mortgage (called a seller take-back mortgage) at a rate of 8%, provided the loan is paid off in full in 3 years. You expect to inherit $210,000 in 3 years, but right now all you have is $21,000, and you can afford to make payments of no more than $24,000 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 was amortized over 3 years, how large would each annual payment be? Do not round intermediate calculations. Round your answer to the nearest cent.

Could you afford those payments?

If the loan was amortized over 30 years, what would each payment be? Do not round intermediate calculations. 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? Do not round intermediate calculations. Round your answer to the nearest cent.

What would the balloon payment be? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

These is a lot of calculation involved in this. If you have a financial calculator or excel, it would be easy for you to solve this. The concept is based on discounting.

r= 0.08

loan's present value (pv) = 189000

time period (nper) = 3 years

Therefore, the equal yearly instalments will be (=pmt function in excel) 73338.33

The equation is 189000 = pmt/(1.08)+pmt/(1.08^2)+pmt/(1.08^3) which gives us $73338.33

As we can only afford $24000 per year we cannot afford it.

Now time period (nper) changes to 30. If done in excel, you can make adjustments to get the answer as $16788.38.

This amount we can afford as per the question.

After three years the amount we have to pay as balloon payment can be found by using excel as following -

Use =pv function in excel. nper will be 27. PMT will be 16788.38. Just ignore the negative sign excel shows. Answer will be $ 183583.70