On 1 January 2015, Peter will retire. He has paid an instalment of 20,000 EUR on 1 January 2000 and after that, he makes annual payments of 2,000 EUR every year up to 2014 on 1 January. The bank offers 5 per cent p.a. over the whole period.

(a) What is the amount on 1 January 2015?

(b) Beginning with 31 January 2015, Peter wants to make a monthly withdrawal of 500 EUR. What is the present value of the annuity after ten years? Interest is compounded monthly at a rate of 5 per cent p.a.