MATH 2FM3 Lecture Notes - Lecture 14: The Monthly

• School: McMaster University
• Department: Mathematics
• Course: MATH 2FM3
• Professor: Petar Jevtic

Document Summary

3. 1. 3 retrospective form of the outstanding balance: recursively we nd the successive outstanding balances as follows. Ob2 = ob1(1 + i) k2 = ob0(1 + i)2 k1(1 + i) k2 so following this pattern we nd. Obt = ob0(1 + i)t k1(1 + i)t 1 k2(1 + i)t 2 kt, (1) which is the retrospective method of forming the outstanding balance just after the tth payment. Obn = ob0(1 + i)n k1(1 + i)n 1 k2(1 + i)n 2 kn = 0. Obn n = l k1 k2 2 kn n = 0. 3. 1. 4 prospective form of the outstanding balance: by replacing ob0 with l = k1 + k2 2 + + kn n in equation (1) we get. Obt = (1 + i)t[k1 + k2 2 + + kn n] . K1(1 + i)t 1 k2(1 + i)t 2 kt. = kt+1 + kt+2 2 + + kn n t.