1. A loan of $1,000,000 repayable at 5% interest over 20 years by a varying annuity is repaid with the amount of capital repaid each period being a constant amount of $50,000 pa.
   1. Derive a general formula for the annual annuity installment amount.
   2. Derive the value of the 1^st installment payable at time one.
   3. Derive the PV of the amount owed at time 10 just after making the 10^th payment.