Question

Assume a fixed rate mortgage [FRM] loan is made in an amount of $100,000 at a nominal interest rate of 7% for a term of 30 years

1] If the mortgage is a Fully Amortizing [FA], what is the Monthly Payment ?
2] If the mortgage is a Partially Amortizing [PA] , what is the Monthly Payment? Suppose a balloon payment at maturity of $50,000
3] If the mortgage is a Zero Amortizing [IO], what is the Monthly Payment ?
4] If the mortgage is a Negative Amortizing [NA], what is the Monthly Payment ? Suppose a balloon payment at maturity of $120,000

Answer 1

1) For a fully amortizing loan, the monthly payment is approximately $665.30. 2) For a partially amortizing loan, the monthly payment is $583.33. 3) For a zero amortization loan, the monthly payment is approximately $583.33. 4) For a negative amortization loan, let's assume a monthly payment of $500, resulting in the loan balance increasing.

Step-by-step explanation:

1) If the mortgage is a Fully Amortizing (FA)

Using the formula for monthly payment on a fully amortizing loan:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))

Applying the formula, we get:

Monthly Payment = (100,000 * 0.07/12) / (1 - (1 + 0.07/12)^-(30*12))

Monthly Payment ≈ $665.30

2) If the mortgage is a Partially Amortizing (PA)

For a partially amortizing loan, the monthly payment only covers the interest, while the principal remains partially unpaid. So, the monthly payment in this case will be the interest amount which is $583.33.

3) If the mortgage is a Zero Amortizing (IO)

For a zero amortization loan, the monthly payment only covers the interest. In this case, the monthly payment is calculated using the formula:

Monthly Payment = (Loan Amount * Monthly Interest Rate)

Applying the formula, we get:

Monthly Payment = (100,000 * 0.07/12)

Monthly Payment ≈ $583.33

4) If the mortgage is a Negative Amortizing (NA)

For a negative amortization loan, the monthly payment is less than the interest amount, resulting in the unpaid interest being added to the principal. Let's assume a monthly payment of $500. In this case, the loan balance will increase instead of decreasing.