The possibility to create repayment schedules is virtually limitless. In this paragraph some other techniques, although not very common, are presented.

4.5.1 Negative Amortizing Constant Payment Loan

In a negative amortizing constant payment loan the borrower and the lender negotiate a loan agreement according to which the outstanding loan balance at the end of the loan term will be greater than the loan amount itself and thus the periodic payment will be lower than the interest amount due periodically. The outstanding loan value at the end of the loan term will be simply the sum of the loan amount plus all the annual differences between the interest payments and the monthly payments.

EXAMPLE 4.9

In the example in Figure 4.11 the borrower takes out a loan amount of €100,000 at a nominal yearly interest rate of 6% for a 20 year period. The final amount owed at the end of the loan period will be €125,000 and thus the monthly payment is €431.62.

Negative Amoritizing, Costant Payment Mortage

Loan Amount

€ 100,000

Maturity (years)

20

Interest rate (annual)

6%

Interest rate (monthly)

0.49%

Final payment

€ 125,000

Fixed Monthly Payment

€ 431.62

FIGURE 4.11 Negative amortizing loan

Monthly payments (CP) and the remaining components of this loan agreement can be easily calculated by using the same formula of the present value of an annuity used for the previous illustration of the partially amortizing, constant payment loans, again solving the formula for CP setting PV = €100,000 and this time BP = €125,000.

4.5.2 Declining Payment Loan with Constant Amortizing

In this variant of repayment, the constant amortization of the loan amount is first computed. The monthly payment is then calculated as the sum of this constant amortization plus the interest payment on the outstanding loan balance at the beginning of the period. The monthly payment will be decreasing to a value close to the amortization value.

EXAMPLE 4.10

Figure 4.12 shows an example where a borrower takes out a loan for €100,000 for a 20 year term at an annual nominal interest rate of 6%. The amortization will be equal to €416.67.

Constant Amortizing Loan

Loan Amount

€ 100,000

Maturity (years)

20

Interest rate (annual)

6%

Interest rate (monthly)

0.49%

Amortization

€416.67

FIGURE 4.12 Constant amortizing loan

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