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Here some plots showing the interests you pay to a bank. Notation:

  • $D$ : loan amount
  • $R$ : monthly installment
  • $I$ : nominal annual interest rate
  • $i = \frac{I}{12}$ : monthly interest rate, 30/360 convention
  • $N$ : total number of installments
  • $T = D + Z$ : total paid (loan + interests)
  • $Z$ : total interests paid

For the $n$-th installment:

  • $d_n$ : debt left after the $n$-th installment ($d_0=D$)
  • $p_n = R - i\,d_{n-1}$ : principal part of the $n$-th installment
  • $z_n = i\,d_{n-1}$ : interest part of the $n$-th installment

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