5.11 Loan Repayments (1/3) A loan is taken out for $200 000 at 7.2% p.a. over 30 years. What is the monthly repayment (M)? Months = 30 yrs x 12 = 360 months Months Interest = 7.2% p.a. ÷ 12 = 0.6% monthly For Month 1: A1 = 200 000 (1.0061) - M For Month 2: A2 = A1 (1.0061) - M A2 = [200 000 (1.0061) – M] (1.0061) - M = 200 000 (1.0062) – M(1.0061) - M = 200 000 (1.0062) – M(1.0061 + 1)

5.11 Loan Repayments (2/3) For Month 3: A3 = A2 (1.0061) - M A3 = [200 000 (1.0062) – M(1.0061 + 1)](1.0061) - M = [200 000 (1.0063) – M(1.0062 + 1.0061) - M = [200 000 (1.0063) – M(1.0062 + 1.0061 + 1) For Month 360 ($0): A360= 200 000 (1.006360) – M(1.006359 + 1.006358 + … + 1.0061 + 1) = 0 M(1.006359 + … + 1.0061 + 1) = = 200 000 (1.006360) M = 200 000 (1.006360) ÷ (1.006359 + … + 1.0061 + 1)

5.11 Loan Repayments (3/3) GP = 1 + 1.0061 + 1.0062 + … + 1.006359 + 1.006360 a(rn – 1) a = 1 n = 360 r = 1.006 Sn = r – 1 a(rn – 1) 1.006360 – 1 S360 = = r – 1 0.006 200 000 x 1.006360 1 + 1.0061 + … + 1.006358 + 1.006359 M = 1.006359 – 1 0.006 = 200 000 x 1.006360 ÷ 200 000 x 1.006360 x 0.006 1.006359 -1 = = $1 366.80