Lessons 6–10 cover annuities, present value, annuity due timing, and technology methods. This checkpoint tests your ability to calculate and compare annuity scenarios, transpose formulas, and interpret financial decisions. Aim for 80%+ before moving to Inquiry Question 3.
Q1. The future value of an ordinary annuity is $FV = a \\times [(1+r)^n - 1]/r$. Answer: B
Q2. $r = 0.072/12 = 0.006$, $n = 36$. $FV = 400 \\times [(1.006)^{36} - 1]/0.006 = \\$16{,}178.63$. Answer: C
Q3. The present value formula is $PV = a \\times [1 - (1+r)^{-n}]/r$. Answer: A
Q4. $PV = 800 \\times [1 - (1.005)^{-48}]/0.005 = \\$34{,}042.55$. Answer: D
Q5. Annuity due = ordinary $\\times (1+r)$. The factor is $(1+r)$. Answer: C
Q6. $PV_{\\text{due}} = 500 \\times [1 - (1.004)^{-24}]/0.004 \\times 1.004 = \\$11{,}346.56$. Answer: B
Q7. Interpolation between 4% (11.118) and 5% (10.380): $11.118 + 0.3 \\times (10.380 - 11.118) = 10.897$. Answer: A
Q8. =PV(0.05, 10, -1000) returns the present value. Answer: D
Q9 (3 marks): (a) $FV = 600 \\times [(1.03)^{10} - 1]/0.03 = \\$6{,}878.33$ [1]. (b) $FV_{\\text{due}} = 6{,}878.33 \\times 1.03 = \\$7{,}084.68$ [1]. (c) Each payment earns one extra period of interest [1].
Q10 (3 marks): $PV = 1{,}200 \\times [1 - (1.005)^{-60}]/0.005 = \\$62{,}034.45$ [2]. This is the maximum purchase price [1].
Q11 (4 marks): (a) $PV_{\\text{ord}} = 500 \\times [1 - (1.006)^{-36}]/0.006 = \\$16{,}028.15$ [1]. $PV_{\\text{due}} = 16{,}028.15 \\times 1.006 = \\$16{,}124.32$ [1]. (b) Difference = $\$96.17$ [1]. (c) The tenant saves money with ordinary payments; the landlord receives more value with due payments [1].
Tick when you've finished all questions and reviewed your answers.