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: $P = \dfrac{L}{a_{\overline{n}|i}}$
Interest in payment t: $I_t = P\left(1 - v^{\,n-t+1}\right)$
Principal in payment t: $P_t = P\,v^{\,n-t+1}$
Principal repayments grow: $P_{t+1} = P_t(1+i)$
Totals: $\sum_{t=1}^{n} P_t = L, \qquad \sum_{t=1}^{n} I_t = nP - L$

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: $D = \dfrac{L}{s_{\overline{n}|j}}$ j is the rate the fund earns
Total outlay: $\text{Total} = Li + D$
Equivalent amortisation: $Li + \dfrac{L}{s_{\overline{n}|j}} = \dfrac{L}{a_{\overline{n}|i}} \iff i = j$
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.