An annuity scheme attracts interest at a monthly compounded rate of 10% per annum. It is intended to make 20 equal annual payments to this fund, with the objective of securing a future amount of £300000. The fund contains an amount of £10000 when the first payment is made.

(a) Calculate the required size of the 20 equal annual payments if:

(i) the future sum is to be available immediately after the last payment is made;

(ii) the future sum is to be available one year after the last deposit is made.

(b) Repeat both of these calculations if the account were empty when the first annuity payment is made.

(c) Suppose that the value of the account when the first payment is made is £50000.

Calculate the size of the 20 equal annual payments that are required to supply the future value of £300000 immediately after the last deposit is made.