ACTSC231 Study Guide - Midterm Guide: Real Interest Rate, Compound Interest, Interest

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Ak(0) = k: e ective rate of interest. Ak(t1) a(t2) a(t1) a(t1) i[t1,t2] : simple interest: a(t) = 1 + st; ak(t) = k(1 + st), compound interest: a(t) = (1 + i)t; ak(t) = k(1 + i)t t 0, simple discount: (1 + i)(1 d) = 1, v : nominal rate of interest (cid:18) (cid:18) (cid:19)m (cid:19)m 1 (cid:19)mt. I(m) = m[(1 + i) 1 m 1] (cid:18) D(m) = m(cid:0)1 (1 d) 1 m(cid:1) (cid:19)m (cid:19) mt (cid:19)m (cid:18) (cid:18) 1 d(m) m: constant force of interest, general force of interest. T = d dt a(cid:48)(t) a(t) (cid:19) (cid:19) ln a(t) = (cid:18)(cid:82) t (cid:18) Limm d(m) = limm i(m) = log(1 + i) . I > i(m) > > d(m) > d. Av at t = t2 of at t = t1: (cid:18)(cid:90) t2 (cid:19) = exp: in ation adjusted interest rate (or real interest rate):