Lessons 5–9 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.
8 multiple-choice questions, graded for your checkpoint score with immediate feedback. Then complete 3 written responses; these are saved for you to self-review against model answers and are not included in the MC score.
Suggested time: 35 minutes. Show formula substitutions in written responses. Keep full precision through calculations and round currency once, at the end, to the nearest cent unless a prompt says otherwise. State whether payments occur at period start or end.
Write your working, then open the matching model answer to self-check.
A saver deposits AUD 600 at each month end for 10 months at 3% per month. Find the ordinary-annuity future value, then find the value if each deposit is instead made at the beginning of the month. Explain the difference.
A buyer can afford payments of AUD 1,200 at each month end for 60 months. The monthly rate is 0.5%. Find the maximum present value of these payments.
A contract pays AUD 500 at the beginning of each month for 36 months at 0.6% per month. Find its present value and the difference from an ordinary annuity with the same payment, rate and term.
Question: Which expression gives the future value of an ordinary annuity with end-of-period payment a, periodic rate r and n payments? Key: A. Each end-of-period payment earns interest for a different number of periods; summing the geometric series gives FV=a[(1+r)^n−1]/r.
Question: A student deposits AUD 400 at the end of each month for 36 months. The nominal annual rate is 7.2%, compounded monthly. What is the future value, to the nearest cent? Key: B. r=0.072/12=0.006. FV=400[(1.006)^36−1]/0.006=AUD 16,020.11.
Question: Which expression gives the present value of an ordinary annuity with payment a, periodic rate r and n payments? Key: C. Discounting each end-of-period payment gives PV=a[1−(1+r)^−n]/r.
Question: A contract pays AUD 800 at the end of each month for 48 months. The monthly rate is 0.5%. What is the present value, to the nearest cent? Key: D. PV=800[1−(1.005)^−48]/0.005=AUD 34,064.25.
Question: Payments are made at the beginning rather than the end of each period. How is an ordinary-annuity value adjusted to obtain the corresponding annuity-due value? Key: B. Each payment occurs one period earlier, so its value is multiplied by 1+r. Thus FV_due=FV_ordinary(1+r), and likewise for PV.
Question: A lease requires AUD 500 at the beginning of each month for 24 months. The monthly rate is 0.4%. What is its present value, to the nearest cent? Key: C. First find ordinary PV=500[1−(1.004)^−24]/0.004, then multiply by 1.004 for annuity due: AUD 11,465.93.
Question: A present-value table gives factors 11.118 at 4% and 10.380 at 5% for a fixed term. Linear interpolation at 4.3% gives which factor? Key: D. Move 0.3 of the way from 4% to 5%: 11.118+0.3(10.380−11.118)=10.8966≈10.897.
Question: A spreadsheet is set to end-of-period payments. Which function is appropriate for finding the present value of AUD 1,000 monthly for 10 months at 0.5% per month? Key: A. PV(rate,nper,pmt,fv,type) returns the present value. type=0 (or omitted) means end-of-period payments.
$FV_{\text{ord}}=600\frac{(1.03)^{10}-1}{0.03}=\$6{,}878.33$. $FV_{\text{due}}=FV_{\text{ord}}(1.03)=\$7{,}084.68$. Each beginning-of-month deposit earns one extra month of interest.
$PV=1{,}200\frac{1-(1.005)^{-60}}{0.005}=\$62{,}070.67$. This is the present value under the stated rate, term and end-of-month timing.
$PV_{\text{ord}}=500\frac{1-(1.006)^{-36}}{0.006}=\$16{,}145.37$. $PV_{\text{due}}=PV_{\text{ord}}(1.006)=\$16{,}242.25$. The difference, calculated before rounding, is $\$96.87$.
Tick when you have finished all questions and reviewed your answers.