Introduction | $$B_t | $$\boxed{B_t | A level-payment loan | $$L | $$\boxed{R | \frac | $$i_p | \frac | $$50{,}000 | Interest, principal repayment, and the balance recurrence | $$I_t | $$A_t | $$I_1 | 50{,}000(0.01) | $$A_1 | 1{,}112.22-500 | $$B_1 | 50{,}000-612.22 | Prospective and retrospective balances | L(1+i)^t | Extra principal payments | General payment schedules | A loan with changing interest rates | $$120{,}000 | A payment rule that depends on the outstanding balance | $$A | $$R_t | \frac | $$R_1 | 833.33+0.01(50{,}000) | $$R_ | $$\text | Level payment versus constant principal | Negative amortization | Final actuarial reading

Introduction | Bond cash flows and the value equation | $$P | Valuing a coupon bond | 45 | Yield to maturity as an inverse problem | $$935{,}000 | Book value | $$BV_t | P(1+i)^t | Callable bonds | $$P_s(i) | $$P_{\max}(i) | From price to sensitivity | $$P(i) | $$\frac | $$\frac | Duration and convexity of a cash-flow stream | $$w_j(i) | $$D_{\text{Mac}}(i) | $$D_{\text{mod}}(i) | -\frac | $$C(i) | A general cash-flow example | Specialization to bonds | Portfolio duration and convexity | From sensitivity to immunization | $$W_H(i) | $$\frac | The surplus function and Redington | $$S''(i_0) | An integrated immunization example | The immunization gap | Final actuarial reading

Introduction | Accumulation and discounting | $$\boxed{A(s,t) | $$\boxed{v(s,t) | \frac | $$A(s,t) | $$v(s,t) | $$a(t) | $$A(2,5) | \frac | $$v(2,5) | Equivalent interest-rate conventions | $$d | $$v | $$\delta | $$i^ | $$d^ | From financial factors to monetary values | $$FV | $$PV | 1000(1.06)^4 | Equations of value and focal dates | $$\boxed{\sum_{j=1}^{n}C_j A(t_j,f) | $$A(t_j,f) | $$\sum_ | Replacing two obligations by one payment | $$X | General cash-flow valuation | $$V(f) | $$V(0) | $$V(T) | Solving for an unknown date | $$V_0 | $$12000(1.08)^ | $$x | $$F(x) | From arbitrary cash flows to annuities | $$\boxed | $$\boxed{PV | Immediate and due annuities | $$a_ | $$PV\approx1000(7.721735) | $$\ddot | Accumulated values of level annuities | $$s_ | $$\boxed | Final financial reading

From financial value to actuarial value | $${}_tE_x | A small life table | $$p_x | \frac{l_{x+1}}{l_x},\qquadq_x | 1-p_x | $${}_tp_x | \frac{l_{x+t}}{l_x},\qquad{}_tq_x | $$ | \frac | \frac | $$ | 1-0.9550 | Actuarial discounting: the pure endowment | $$ | $$ | \frac | A temporary life annuity-due | $$\ddot a_ | A temporary life insurance | $$ | $$A^ | An actuarial identity as an audit | $$A^ | 1 | d,\ddot a_ | $$d | Net premium by the equivalence principle | $$\operatorname{APV}(\text{premiums}) | $$P,\ddot a_ | $$P | Reserves: valuing the remaining contract | $${}_tV | \operatorname{APV}_t(\text{future benefits}) | $${}_2V | 100000A^ | The same contract as a pipe workflow | Moving to a benchmark life table | Final actuarial reading