Question

Youu want to buy a house that costs $150,000. You have $15,000 for a down payment, but your credit is such that mortgage companies will not lend you the required $135,000. However, the realtor persuades the seller to take a $135,000 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 $150,000 in 3 years; but right now all you have is $15,000, 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.)

1. If the loan amortized over 3 years, how large would each annual payment be? Round your answer to the nearest cent.

2. If the loan were amortized over 30 years, what would each payment be? Round your answer to the nearest cent.

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.

1.What would the loan balance be at the end of Year 3? Round your answer to the nearest cent.

2. What would the balloon payment be? Round your answer to the nearest cent.

Answer 1

1. Annual payments

Loan amount (P) =135,000

Interest (R) @ 9%

Loan term (n)= 3 years

Annual payments = P*R*(1+r)ⁿ /((1+r)ⁿ -1)  

=135,000*9%*(1+9%)³/ ((1+9%)³-1)

=53,332.39

2. Annual Payments

Loan amount (P) =135,000

Interest (R) @ 9%

Loan term (n)= 30 years

Annual payments = P*R*(1+r)ⁿ /((1+r)ⁿ -1)  

=135,000*9%*(1+9%)³⁰/ ((1+9%)³⁰-1)

=13,140.41

1. Loan balance outstanding at the end of Year 3

Till the end of Year 2, 2 installments have been paid, therefore 28 installments are left to be paid and hence loan amount outstanding at the end of Year 3 i.e, before the payment of 3rd installment will be

Annual payments = P*R*(1+r)ⁿ /((1+r)ⁿ -1)  

13,140.41= P*9%*(1+9%)²⁸/ ((1+9%)²⁸-1)

P= 132,930.05

Loan balance outstanding at the end of Year 3 after payment of 3rd installment will be

= 13,140.41/9%*(1+9%)²⁷/ ((1+9%)²⁷-1)

=131,753.35

2. Amount of ballon payment = 13,140.41+131,753.35 = 144,893.76