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Serial loan

A serial loan has equal repayments. The repayment is the loan divided by the number of periods. Interest is charged on what remains, so the first period has the highest interest and the highest instalment. Each period the remaining loan falls by one repayment, and the interest falls by the interest on one repayment. The instalment therefore becomes smaller and smaller. That distinguishes the serial loan from the annuity loan, where the instalment is constant.

Try it yourself

Geometric series

repayment=Ln\text{repayment} = \frac{L}{n}equal each period
interest=r⋅remaining\text{interest} = r \cdot \text{remaining}decreases

Symbols

LLthe loanNOK
nnnumber of periods
rrinterest per period

Example

A loan of 1,000,000 NOK, 20 years, 5% interest. Repayment 1 000 000/20=50 0001\,000\,000/20 = 50\,000 NOK.

First interest 0.05⋅1 000 000=50 0000.05 \cdot 1\,000\,000 = 50\,000 NOK, so the first instalment is 100 000100\,000 NOK.

It decreases by 0.05⋅50 000=25000.05 \cdot 50\,000 = 2500 NOK per year.

The repayment is fixed. The instalment decreases.
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Part of Mathematics S2: Savings, loans and present value.