Kindly answer the given problems and indicate the detailed steps of the computation including where does the formulas that was being used came from. With the given problems which already has an answer show also its detailed steps of the computation including where does the formulas that was being used came from, for proving the indicated answer. Lastly in each question indicate its cash flow diagram.

1. A stock certificate of a mining company guarantees a dividend of P100 at the end of each year for 10 years, and a final additional payment at the end of 10 years of P1,200. If money is worth 12% effective, what is the certificate worth now? (Ans. P951.39) 2. A business man loans an amount of P100,000 at a local commercial bank 10% effective annual interest. How much is his monthly payment if he is required to pay at the beginning of the first day of the month for a period of 30 years? 3. A certain manufacturing plant is being sold and was submitted for bidding. Two bids were submitted by interested buyers. The first bid offered to pay P200,00 each year for 5 years, each payment being made at the beginning of each year. The second bidder offered to pay P120,000 the first year, P180,000 the second year and P270,000 each year for the next 3 years, all payments being made at the beginning of each year. If money is worth 12% compounded annually, which bid should owner of the plant accept? 4. A man bought an equipment costing P60,000 payable in 12 quarterly payments, each installment payable at the beginning of each period. The rate of interest is 24% compounded quarterly. What is the amount of each payment? (P6751.53) 5. A chemical engineer wishes to set-up a special fund by making uniform semiannual end-of-period deposits for 20 years. The fund is to provide P100,000 at the end of each of the last five years of the 20-year period. If interest is 8% compounded semiannually, what is the required semiannual deposits to be made? (Ans. 6,193.39) 6. A debt of P40,000, whose interest rate is 15% compounded semiannually, is to be discharged by a series of 10 semiannual payments, the first payment to be made 6 months after consummation of the loan. The first 6 payment will be P6,000 each, while the remaining 4 payments will be equal and of such amount that the final payment will liquidate the debt. What is the amount of the last 4 payments? (Ans. P5,454)