You want to buy a house that costs $140,000. You have $14,000 for a down payment, but your credit is such that mortgage companies will not lend you the required $126,000. However, the realtor persuades the seller to take a $126,000 mortgage (called a seller take-back mortgage) at a rate of 5%, provided the loan is paid off in full in 3 years. You expect to inherit $140,000 in 3 years, but right now all you have is $14,000, and you can afford to make payments of no more than $22,000 per year given your salary. (The loan would call for monthly payments, but assume end-of-year annual payments to simplify things.) Required:
a. If the loan was amortized over 3 years, how large would each annual payment be? Could you afford those payments?
b. If the loan was amortized over 30 years, what would each payment be? Could you afford those payments?
c. 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, and what would the balloon payment be?

a. The annual payment if the Mortgage was amortized over three years is $45,315.96 (Interest + Principal)

The Mortgage payments are not affordable because his affordability funds are limited to $22,000 annually.

Annual Amortization Schedule  

 Beginning Balance      Interest             Principal        Ending Balance

1             $126,000.00        $5,393.36        $39,922.60        $86,077.35

2              $86,077.35        $3,350.86          $41,965.10          $44,112.18

3                $44,112.18          $1,203.81           $44,112.15                 $0.00

b.  The annual payment if the Mortgage was amortized over thirty years is $8,116.80 (Interest + Principal)

The Mortgage payments are now affordable with his affordability amount of $22,000 per year.

Annual Amortization Schedule for the first three years:  

 Beginning Balance      Interest           Principal     Ending Balance

1            $126,000.00        $6,257.79        $1,859.01         $124,141.04

2             $124,141.04         $6,162.68        $1,954.12        $122,186.97

3            $122,186.97         $6,062.70       $2,054.10        $120,132.93

c. Payments made by the end of the third year were $5,867.07 with a balance of $120,132.93.

Data and Calculations:

Cost of house = $140,000

Down payment = $14,000

Mortgage value = $126,000($140,000 - $14,000)

Mortgage interest rate = 5%

Affordable annual payments = $22,000

Thus, the balloon payment is always based on an agreed percentage of the loan, which is not provided here.

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Explanation:

Given the following :

Cost of house = $140,000

Down payment = $14000

Take back mortgage = 126000 = PV

Rate (r) = 5%

Yearly payment one can afford = 22000

a. If the loan was amortized over 3 years, how large would each annual payment be? Could you afford those payments?

Number of period = 3

Using the relation:

PMT = r(PV) / 1 - (1 + r)^-n

PMT = 0.05(126000) / 1 - 1.05^-3

PMT = 6300 / (1-0.8638375)

PMT = 46,268.23

He won't be able to afford it, as the monthly payment is larger than the affordable amount of $22000

b. If the loan was amortized over 30 years, what would each payment be? Could you afford those payments?

PMT = r(PV) / 1 - (1 + r)^-n

PMT = 0.05(126000) / 1 - 1.05^-30

PMT = 6300 / (1-0.2313774)

PMT = 8196.48

He would be able to afford it, as the monthly payment is lower than the affordable amount of $22000

c. 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, and what would the balloon payment be?

Present value of remaining balance after the 3rd year:

Present Value (PV) = PMT[(1 - (1 + r)^-n) / r]

Where

PMT = periodic payment = 8196.48

r = Interest rate = 5% = 0.05

n = number of periods = 30 - 3 = 27

PV = 8196.48[(1 - (1 + 0.05)^-27) / 0.05]

PV = 8196.48[(1 - (1. 05)^-27) / 0.05]

PV = 8196.48[0.7321516 / 0.05]

PV = 120,021.32

Balloon payment :

120,021.32 + 8196.48 = 128,217.80

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