1. Derive the formula relating present worth and ordinary annuity using geometric series. 2. How much should I expect a lump sum from a deal at the end of 3 years if I start investing today at amount of Php 2,000.00 every 3 months with a ROR of 1.5% compounded quarterly? Provide complete solution and cash flow diagram. 3. A contract has been signed to lease a building at Php 200,000.00 per year with an annual increase of Php 1,500.00 for 8 years. Payments are to be made at the end of each year starting one year from now. The prevailing interest rate is 7%. What lump sum paid today would be equivalent to the 8-year lease payment plan? Provide complete solution and cash flow diagram.

4. An engineer has to pay for a loaned equipment he purchased for Php 3,000.00 after each month with an interest rate 1% compounded quarterly. On the the 5th year the payment was deferred for 6 months and resumed thereafter but with an increased amount of Php 4,000.00 for the next 2 years. If the interest and compounding apply the same throughout the entire period, how much is the lump sum when the engineer has totally paid the equipment. Provide complete solution and cash flow diagram. 5. A payment is arranged such that the first year requires you to pay Php 1,000.00 as ordinary annuity. The second year requires you to pay at the beginning of each month for Php 1,5000.00. On the third year onwards, how much are you required to pay after each month such that the entire payment's present worth is Php 100,000.00. The interest is said to be 2% compounded bi-monthly applied throughout. Provide complete solution and cash flow diagram.