Loans - Exam FM formula sheet

Every Exam FM formula in loans on one printable sheet, condensed from the 3 reference pages that teach them.

3 topics, 12 formula lines. Every line is condensed from the Exam FM formula pages, which stay free to read in full. Print this page to get the sheet on paper; the site chrome drops away.

What is on this sheet

Loans

Amortisation

Level payment: $P = \frac{L}{a _{\overline{n} ∣ i}}$
Interest in payment t: $I_{t} = P (1 - v^{n - t + 1})$
Principal in payment t: $P_{t} = P v^{n - t + 1}$
Principal repayments grow: $P_{t + 1} = P_{t} (1 + i)$
Totals: $\sum_{t = 1}^{n} P_{t} = L, \sum_{t = 1}^{n} I_{t} = n P - L$

Outstanding balance

Prospective: $B_{t} = P a_{\overline{n - t} ∣ i}$
Retrospective: $B_{t} = L (1 + i)^{t} - P s_{\overline{t} ∣ i}$
Recursion: $B_{t} = B_{t - 1} (1 + i) - P$

Sinking funds

Sinking fund deposit: $D = \frac{L}{s _{\overline{n} ∣ j}}$ j is the rate the fund earns
Total outlay: $Total = L i + D$
Equivalent amortisation: $L i + \frac{L}{s _{\overline{n} ∣ j}} = \frac{L}{a _{\overline{n} ∣ i}} ⟺ i = j$
Net amount owed: $L - D s_{\overline{t} ∣ j}$

Loans - Exam FM formula sheet. Formulas condensed from the free reference pages on this site. Not affiliated with or endorsed by the Society of Actuaries.