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Financial Maths, STD2 EO-Bank 19

The table shows the present value of an annuity with a contribution of $1.

  
 

Rina and Owen each set up an annuity, depositing a fixed amount at the end of every year.

  1. Rina pays $2500 each year for 5 years into an annuity earning 3% per annum, compounded annually. Using the table, find the present value of Rina’s annuity.   (1 mark)
  2. Owen pays $4000 each year for 3 years into an annuity earning 5% per annum, compounded annually. Whose annuity has the greater present value? Justify your answer with calculations.   (2 marks)
Show Answers Only

a.    \(\$11\,449.25\)

b.    \(\text{Rina’s annuity is greater: }\$11\,449.25>\$10\,892.80\)

Show Worked Solution

a.    \(\text{Table factor when}\ n=5,\ r=3\%\ \Rightarrow\ 4.5797\)

\(\therefore\ PVA\ \text{(Rina)}=2500\times 4.5797=\$11\,449.25\)
  

b.    \(\text{Table factor when}\ n=3,\ r=5\%\ \Rightarrow\ 2.7232\)

\( PVA\ \text{(Owen)}=4000\times 2.7232=\$10\,892.80\)

\(\text{Rina’s annuity is greater: }\$11\,449.25>\$10\,892.80\)