We wish to set up an annuity, where the first payment is K500, and each subsequent payment increases by 4.25%. Payments are to be made at the end of each half year for 6 years. If the account in which the principal is invested yields 8.5% p.a. compounded half –yearly;

(a) How much must be invested into the account to pay for the annuity? 

(b) Show by drawing (a full) an appropriate table of values, that the amount in the account is exhausted at the end of the sixth year.