Lessons 11–15 cover recurrence relations, superannuation, loan mathematics, repayment calculations, and extra repayment strategies. This checkpoint tests your ability to model financial situations iteratively, calculate repayments, and compare debt-reduction strategies. Aim for 80%+ before moving to Inquiry Question 4.
Its question set has not been written, so there is nothing here to attempt. Nothing you have done is lost, and the lessons either side of it are unaffected.
To test yourself on this material now, use the module quiz, which covers the same content.
Q1. The investment recurrence is $A_{n+1} = (1+r)A_n + a$. Answer: A
Q2. $A_1 = 1.005(5{,}000) + 200 = 5{,}225$. Answer: C
Q3. Net return = gross return - fees = 7% - 1.2% = 5.8%. Answer: B
Q4. The loan recurrence is $A_{n+1} = (1+r)A_n - M$. Answer: D
Q5. $M = 400{,}000 x 0.004167 / [1 - (1.004167)^{-360}] = \\$2{,}147.29$. Answer: B
Q6. $P = 2{,}000 x [1 - (1.004)^{-240}] / 0.004 = \\$303{,}000$ (approx). Answer: C
Q7. Offset reduces the balance on which interest is calculated. Answer: A
Q8. $n = -\ln(1 - 250{,}000 x 0.005/1{,}800) / \ln(1.005) = 196$ months ≈ 16.3 years. Answer: B
Q9 (3 marks): (a) $A_{n+1} = 1.006A_n + 150$ [1]. (b) $A_1 = 1.006(4{,}000) + 150 = \\$4{,}174$ [1]. $A_2 = 1.006(4{,}174) + 150 = \\$4{,}349.04$ [1].
Q10 (3 marks): (a) $C = 80{,}000 x 0.115 = \\$9{,}200$ [1]. (b) $r_{net} = 7% - 1% = 6%$ [1]. (c) $A_{30} = 20{,}000(1.06)^{30} + 9{,}200 x [(1.06)^{30} - 1]/0.06 = 114{,}870 + 726{,}340 = \\$841{,}210$ [1].
Q11 (4 marks): (a) $M = 300{,}000 x 0.005 / [1 - (1.005)^{-240}] = \\$2{,}149.29$ [1]. (b) Total repaid = $2{,}149.29 x 240 = \\$515{,}830$ [1]. Total interest = $515{,}830 - 300{,}000 = \\$215{,}830$ [1]. (c) With $3{,}000/month: n = -\ln(1 - 300{,}000 x 0.005/3{,}000) / \ln(1.005) = 126$ months = 10.5 years. Saves 9.5 years [1].
Tick when you've finished all questions and reviewed your answers.