Linear Loan

Repayment type: linear

Also known as: Tilgungsdarlehen, Abzahlungsdarlehen, Ratendarlehen, straight-line loan, equal-principal loan

Each period repays the same principal amount, and interest is charged on the falling balance. Installments therefore start high and decrease over the term. Total interest is lower than for an annuity loan of the same size, at the price of higher early payments. Common for machinery and vehicle finance and for promotional loans.

How it works

1. Formula

$$P = \frac{B_0}{n}$$ $$I_t = B_{t-1} \cdot r$$ $$A_t = P + I_t$$

where $P$ is the principal per period, $B_0$ the principal, $n$ the number of installments, $r$ the interest rate per period, $B_{t-1}$ the balance before period $t$, $I_t$ the interest and $A_t$ the installment in period $t$.

2. With the terms

$$\text{Principal per period} = \frac{\text{Principal}}{\text{Number of installments}}$$ $$\text{Interest} = \text{Previous balance} \cdot \text{Rate per period}$$ $$\text{Installment} = \text{Principal per period} + \text{Interest}$$

3. With the example numbers: 100,000 EUR, 4.00 % p.a. with one installment per year, 5 installments.

$$P = \frac{100{,}000}{5} = 20{,}000.00$$ $$I_1 = 100{,}000 \cdot 0.04 = 4{,}000.00$$ $$A_1 = 20{,}000.00 + 4{,}000.00 = 24{,}000.00$$

Year 2 starts from the lower balance of 80,000: $I_2 = 80{,}000 \cdot 0.04 = 3{,}200.00$ and $A_2 = 23{,}200.00$.

Example

100,000 EUR at 4.00 % p.a., 5 years, one installment per year.

Compared with the annuity loan on the same terms, the linear loan pays 313.55 less interest but asks for 1,537.29 more in year one.

In LoanMonitor

• Wizard, Terms: repayment type Linear. The principal per period follows from the principal and the number of installments.
• If the contract fixes the principal portion as an amount instead, open Adjustments → Repayment plan and add a plan change with the method Fixed principal and that amount. A remaining balance at maturity is shown in the schedule.

Related

• Loan Types overview
• Annuity Loan
• Bullet Loan