There is a mistake in the numerical answer for Q5 (a). It should be 1452.259126.

Your equation of value should look like :

PV=1+4v+9V^2...+20V^19

multiplying this by v you get : v+4v^2+...20v^20

(PV-vPV)=1+3v+5v^2+ 39v^19-20v^20

The terms on the right can be broken up into an annuity in advance for 20 years plus 2 times an increasing annuity in arrears for 19 years minus 400v^20.

You can then solve for PV at an interest rate of 5% p.a.

For question (b): the rate of payment is continuous over the year. Therefore setting the equation of value up from first principles should give you the same equation as in (a) just multiplied by a continuously payable annuity for 1 year.

The answer is therefore (1452.259126 x 0.975996872 = 1417.40) the correct numerical answer given in the solutions.