Can someone correct any errors in the workings in red, particularly part 2 (Please show written equations, no excel!)

A payment schedule requires 25 annual payments of $20,000, the first payment to be made 10 years from today. Using a discount rate of 8%, what is the present value of this series of payments? (2 marks) (1 - (1+r)-") PV = PG ((1 + r)t-1 xr) t = 10 r = 8% - P = $20,000 - n=25 (1 - (1 + 0.08)-25) PV = 20,000 ((1 + 0.08)10-10.08) 1- - 1.08)-25) PV = 20,000 1.0810-1 0.08 0.853982 PV = 20,000 0.159920 PV = 106800.92 2. Assume the payment schedule in problem 1 changes as follows: the payment 15 years from today is waived, and . a payment of $30,000 is made 18 years from today. The other payments are unchanged. Using a discount rate of 10%, what is the present value of this series of payments? (2 marks) Step 1: deferred annuity PV = PG (1 - (1+r)-") ((1+r)-1 xr) P = $20,000 n=25 t = 10 r = 10% PV = 20,000 (1 - (1 + 0.1)-25) ((1+ 0.1)10-1 0.1) 1 - 1.1)-25) PV = 20,000 1.110-1 0.1 0.907704 PV = 20,000 0.235795 PV = 76991.02 Step 2: adjusting for waiver at year 15 Step 3: adjusting for additional payment at year 18 P PV (1+r)" Additional payment = 30000 - 20000 PV = 20000 (1 + 0.1)15 Additional payment = 10000 PV = 20000 PV = 4.177248 P (1+r)" PV = 4787.84 PV = 10000 (1 + 0.1)18 10000 PV = 5.559917 PV = 1798.59 Adjusted payment schedule: PV = 76991.02 - 4787.84 + 1798.59 PV = 74001.77