ANNUITY 1. What are the present worth and the accumulated amount of a 10-year annuity paying P10,000 at the end of each year, with interest at 15% compounded annually? 2. What is the present worth of P500 deposited at the end of three months for 6 years if the interest rate is 12% compounded semi-annually. 3. A business man needs P50,000 for his operations. One financial institution is willing to lend him the money for one year at 12.5% interest per annum (discounted). Another lender is charging 14%, with the principal and interest payable at the end of one year. A third financier is willing to lend him P50,000 payable in 12 equal monthly instalments of P4,600. Which offer is best for him? 4. A man invests P10,000 now for the college education of his 2-year old son. If the fund earns 14% effective, how much will the son get each year starting from his 18th to the 22nd birthday? 5. If P10,000 is deposited each year for 9 years, how much annuity can a person get annually from the bank every year for 8 years starting 1 year after the 9th deposit is made. Cost of money is 14%. 6. A debt of P40,000, whose interest rate is 15% compounded semi-annually, is to be discharged by a series of 10 semi-annual payments, the first payment to be made 6 months after consumption of the loan. The first 6 payments will be equal and such amount that the final payment will liquidate the debt. What is the amount of the last payments? 7. A farmer brought a tractor costing P25,000 payable in 10 semi-annual payments, each instalment payable at the beginning of each period. If the rate of interest is 26% compounded semi-annually, determine the amount of each instalment. How much money will he save if he paid the tractor in cash? 9. A woman loans P987,499 from a bank with interest at 5% cpd. semi-annually. She agrees to pay her obligations by paying 8 equal annual payments, the first being due at the end of 13 years. Find the annual payments. 11. A man loans P187,499 from a bank with interest at 5% cpd. annually. He agrees to pay his obligations by paying 8 equal annual payments, the first being due at the end of 10 years. Find the annual payments. 8. A man decides to set aside P50 at the end of each month for his child’s college education. If the child were to be born today, how much will be available for its college education when he/she turns 19 years old? Assume an interest rate of 5% compounded monthly. 10. At age 20, a man decided you want to invest on Life Insurance. He found an offer that provides 5% cpd. annually. He wants to give P200,000 per year for the next 40 years. At age 60, how much would he have saved up by then? 12. While walking around manila, a man stumbled upon a Jeep Dealer shop. He went inside and inquired for the latest model of the Jeep Wrangler. He was told that the price was at P4.4 Million if he would buy it in cash. Interested in buying it, he asked for a loan from a bank, charging him an interest of 3% annually, and he was required to make an equal annual payment for 5 years starting a year from now. How much is he going to pay if the future value of the loan is P 5 Million. 13. What are the present worth and the accumulated amount of a 10-year annuity paying 10,000 at the end of each year, with the interest at 15% compounded annually? 15. If Php 25,000 is deposited now into a savings account that earns 6% per year, what uniform annual amount could be withdrawn at the end of each year for ten years so that nothing would be left in the account after the 10th withdrawal? Php 3725.74 17. If you’re planning to franchise a certain food cart business worth Php 150,000, two years from now but you’re current capital does not meet this requirement. Instead, you’ll make twenty-four monthly deposits into an account paying 8% nominal interest rate compounded monthly, how much should the deposit be so that after two years you will be able to avail the franchise? Php 5784.09 14. Determine the present equivalent value of Php 5,000 paid every 3 months for a period of seven years and rate of interest is 12% compounded quarterly? Php 93,820.40 16. An engineer wants to start a business which requires purchase of a Php 100,000 worth machine which will produce a net income of Php 11,000 per year after deducting operating expenses. The engineer plans to put the machine on sale after 4 years, what must be the resale price to justify the investment if the engineer should make 12% annual return on the investment. Php 104,779.33 18. How much money would you have to deposit for five consecutive years starting one year from now if you want to be able to withdraw Php 50,000 ten years from now? Assume i = 14% compounded annually. Php 3,928.60 19. A corporation disbursements: will make the following a. Php 50, 000 on December 31, 1991 b. Php 100,000 on December 31, 1992 c. Php 200,000 one December 31, 1993 21. A man invested Php 10,000 now for the college education of his three-year old son. If the fund earns 14% effective, how much will the sun get each year starting from 19th to 22nd birthday? 23. A farmer bought a tractor costing Php 25,000 payable in ten semi-annual payments, each installment payable at the beginning of each period. If the rate of interest is 26% compounded semi-annually, determine the amount of each installment. Php 4077.20 22. During the first ten years of the life of a certain machine, the following were spent for its maintenance: 24. A certain manufacturing plant is being sold and was submitted for bidding. Two bids were submitted by intrsted buyrs. The first bid offered to pay Php 200,000 each year for 5 years, each payment being made at the beginning of each year. The second bidder offered to pay Php 120,000 the first year, Php 180,000 the second year and Php 270,000 each year for the next 3 years, all payments being made at the beginning of each year. If money is 12% compounded annually, which bid should the owner consider? To accumulate these sums, a singking fund is established by making equal year-end deposits starting December 31, 1986 up to the end of 1993. If the fund earns 9% interest compounded annually, what is the required amount of the annual deposit? Php 33, 404.89 20. What lump sum of money must be deposited in a bank account at present time so that Php 500 per monthly can be withdrawn for five years with the first withdrawal scheduled six years from today? Interest rate is 9% compounded quarterly. Php 14,170.27 During the first 5 years, Php 3,000 was spent each year; during the second five years, Php 5,000 each year was spent. In addition, Php 8,000 was spent for overhauling at the end of the fourth year and Php 10,000 also for averhauling at the end of the ninth year. If money is worth 9% compounded annually, what was the equivalent uniform annual cost for the ten-year period? Php 5388.36 25. P6, 200.00 debts bear interest at 8% compounded annually. It is to be repaid in annual payments of P1, 000.00 each. a. How many payments must the debtor make? (8.9) b. How much will be the final payment if it is made one year the last P1, 000.00 payments. (P906.27) 26. A P10, 000 loan is to be paid off in 10 equal annual payments. The annual interest rate is 15%. How much interest will be paid in the first two years? 27. The monthly rent of a house is P9, 000.00 payable at the beginning of each month. If money is worth 12% compounded monthly, what is the cash equivalent of 5 years rent? 29. Five thousand pesos is deposited at the end of each year for 15 years into an account earning 7.5% compounded continuously. Find the amount after 15 years. 28. What sum should be invested at the beginning of each quarter, at 16% compounded quarterly in order to have P25, 000.00 in a fund in 10 years. 30. A man made a year-end payment of P100, 000 to an account earning 7% annually for 10 years. How much is in the account after 20 years? 31. Find the present value of 10 payments at P100.00 each if the first payment is due at the end of 3 ½ years and if money is worth 12% compounded semi-annually. (P518.85) 32. If money is worth 8% compounded quarterly, find the present value of a P100.00 annuity every 3 months, the first of which is due at the end of 4 years and the last at the end of 10 years. 33. If money is worth 7% effective, find the present value of a P4, 000.00 perpetuity payable every year. (P57, 142.86) 34. What sum when invested at 12% compounded semi-annually will provide P850.00 indefinitely at the beginning of every 6 months? (P1, 016.67) 35. Find the present value of quarterly payments of P1000.oo that start at the end of 3 ¼ years and continue indefinitely, if money is worth 16% compounded quarterly. (P15, 614.00) 36. 1. STL service and installation works purchased a diesel generator from the ABB Electric Company valued at P2, 500. 000.00 on an easy payment plan, as follows: 20% cash upon delivery of the unit and the balance to be paid in 24 monthly installments with 12 % nominal interest on the unpaid balance. a. How much would the STL pay each month to the ABB Electric Co.? b. If instead of the above terms, the STL decided to start a sinking fund to enable it to purchase the same motor after 2 years on cash basis at the same value less 10% discount for cash purchase, how much would the monthly deposit in the fund be, if the money will earn interest at 6%. Assume interest rates are compounded monthly . 37. You need a P70, 000.00 per year for four years to go to college. Your father invested an amount of P100, 000.00 in a 7% account for your education when you were born. If you withdraw the money worth P70, 000.00 at the end of your 18th, 19th, 20th and 21st years, how much much money will be left in the account at the end of your 22nd year?
