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Annuity and serial loans

An annuity loan has equal instalments through the whole term, where the interest portion decreases and the principal portion increases over time. A serial loan has equal principal payments, so the instalment shrinks as the debt decreases — giving lower total interest than an annuity loan with the same rate and term.

A = P\,\frac{r}{1-(1+r)^{-n}}

instalment in an annuity loan

Symbols

$P$	loan amount	kr
$r$	rate per period
$n$	number of periods
$A$	instalment (annuity payment)	kr

Example

Loan 500,000 kr, 3% interest, 10 years:

$A = 500000\cdot \dfrac{0.03}{1-1.03^{-10}} \approx 58.615$ kr per year.

Annuity loans give predictable instalments, serial loans give the lowest total interest cost.

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Part of Engineering Economics: Investment analysis.