The Institute of Chartered Accountants of Sri Lanka

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1 The Institute of Chartered Accountants of Sri Lanka Executive Diploa in Business and Accounting Financial Matheatics Financial Matheatics deals with probles of investing Money, or Capital. If the investor (an individual investor or copany) puts soe capital to an investent, a financial return will be expected. Investors ay wish to know how uch return will be obtained by investing oney now for a given period or how uch return will be obtained in n years tie by investing soe oney every year for n years. The two ajor techniques of financial atheatics are copounding and discounting. These techniques are very closely related to each other Siple Interest Siple interest is interest calculated on the principal only and which is a given proportion of original investent and duration. I prn Where I = Interest per period r = Interest rate n = the duration (norally years) P = Original su invested Exaple : How uch will an investor have after five years if he invests Rs.1,200 at 10% siple interest per annu?. Nishantha Palihawadana Page 1

2 2.1.2 Copound Interest The process of accuulating interest on interest on the investent over tie. That is if a su of oney, the principal, is invested at a fixed rate of interest such that the interest is added to the principal and no withdrawals are ade, then the aount invested will grow by an increasing in each successive tie period, since interest earned in earlier periods will itself earn interest in later periods. A p(1 r) n Where A: The Su invested after n periods p : the original su invested n : the nuber of periods r : the annual interest rate if copounding has taken place several ties per year: r A p(1 ) n where is the nuber of ties copound per year. 2.2 Continuous copounding If your nuber of copounding periods per year becoes infinite, then interest is copounded continuously. A pe rn 2.3 Discounting (present value) Discounting is the reverse of copounding. Its ajor application in business is in the evaluation of capital expenditure projects, to decide whether they offer satisfactory return to the investor. r n A P(1 ) r Fv Pv(1 ) Fv Pv r n (1 ) n Page 2 of 7

3 2.4 Net Present value The net present value (NPV) ethod works out the present values of all ites of incoe and expenditure related to an investent at a given rate of return, and then works out a net total. If it is positive, the investent is considered to be acceptable. If it is negative, the investent is considered to be unacceptable. 2.5 Annuity An annuity is a finite set of sequential cash flows, all with the sae values. Value of the ordinary annuity Ordinary annuity has the first cash flow that occurs at the end of the first period V a n P (1 r / ) 1 where p: annuity aount n: duration (Years) r: the interest rate : nuber of copound per year Value of the annuity due Annuity due has a first cash flow that is paid iediately V a n P (1 r / ) 1 (1 r / ) Present value of the ordinary annuity n p1 (1 r / ) Pva Present value of the annuity due n p1 (1 r / ) Pva (1 r / ) Page 3 of 7

4 Depreciation Depreciation on reducing balance ethod can be calculated as follows: Nv Cost(1 r) n Where Nv = Net value of the asset r: Depreciation percentage Exercise: 1. A person is interested to invest Rs. 12,000 at a siple interest rate of 12% per annu. Calculate the interest he would have earned at the end of five years. 2. A person has borrowed Rs. 16,800 at a siple interest rate of 10% per annu fro a copany and settled after three years and six onths. Find the aount he would have paid as interest at the end of this period. 3. A person gave a loan of Rs. 80, 000 at 10% siple interest rate to a friend. How long he has to wait to receive a total aount of Rs 200,000? 4. Mr. Fenando received Rs.27,200 after three years of depositing a su of oney in a bank which provides 12% siple interest. How uch is the aount deposited originally. 5. A su of Rs. 400,000 is invested on Siple interest, partly at 10% p.a. and partly at 12% p.a. if the total incoe is Rs. 42,000 per annu; find the aount invested at 10% p.a. 6. A client invests Rs. 500,000 in a bond fund projected to earn 7% copounded annually. Estiate the value of her investent after 10 years. 7. A person has deposited Rs. 14,600 in a financial Institute at a annual copound interest rate of 8% for three years. What would be the total value and interest after this period. 8. A client has a Rs. 5 illion portfolio and invests 5% of it in a oney arket fund projected to earn 3% copounded annually. Estiate the value of this portion of his portfolio after seven years. 9. Find the interest rate necessary for Rs. 20,000 to occur to Rs.50,000 in 12 years under copound interest. 10. The finance anager has invested soe oney in a oney arket project. The aount will be doubled after 8 years. Copute the interest rate. Page 4 of 7

5 11. A financial institute provides 8% copound interest rate per year. How any years will it require to double the invested oney. 12. Rs.125,000 was invested in a bank where annual interest rate is 18%. If the bank copound interest onthly what would be the total value after 3 yeas and nine onths. 13. A copany wishers to borrow oney fro a bank. Three banks have quoted different interest rates. Bank A will lend the oney at 18.2% per year copounded quarterly. Bank B will lend at 18.4% per year copounded sei-annually. Bank C will lend oney at 19% copounded annually. Fro which bank should the copany borrow the oney? 14. A person wants to deposit Rs.400, 000 for three years in order to earn soe interest incoe. He can deposit in bank A at 12% per annu on siple interest and in bank B at 10% p.a. on copound interest. Advice hi with necessary calculations, including which is ore beneficial to hi. 15. For liquidity purposes, a client keeps Rs. 100,000 in a bank account. The bank quotes a stated annual interest rate of 12 percent. The bank s service representative explains that the stated rate is the rate one would earn if one were to cash out rather than invest the interest payents. i) With quarterly copounding, how uch will your client have in his account at the end of one year, assuing no additions or withdrawals? ii) With onthly copounding, how uch he have in his account at the end of one year, assuing no additions or withdrawals? iii) With continuous copounding, how uch will he have in his account at the end of one year, assuing no additions or withdrawals? 16. A bank quotes a rate of 5.89 percent with an effective annual rate of 6.05 percent. Does the bank work with annual, quarterly, or onthly copounding? 17. A copany invest Rs.100,000 and earned Rs.40,000 in the year 1 and Rs in the year 2 and Rs. 20,000 in year 3. If the cost of capital of the copany is 12%. Calculate the net present value. 18. What would be the present value of Rs. 60,480 which will be receivable in 4 years fro today. The discount rate for the period would be 8% per annu. Page 5 of 7

6 19. A copany invest Rs.100,000 and earned Rs.40,000 in the year 1 and Rs in the year 2 and Rs. 20,000 in year 3. If the cost of capital of the copany is 12%. Calculate the net present value. 20. To cover the cost of higher education for his two children, a father will ake a Rs. 75,000 payent five years fro now. How uch will he need to invest today to eet his tuition fee, if the investent earns 6 percent annually? 21. A copany is wondering whether to spend Rs. 180, 000 on an ite of equipent, in order to obtain cash profit as follows. Year Cash inflows 1 60, , ,000 If the copany requires a return of 10% per annu, is the project viable 22. The cash flows of the two projects are given below: Year Details Project x Project y 0 Investent 120, ,000 1 Net incoe 80,000 40,000 2 Net Incoe 40,000 50,000 3 Net Incoe 40,000 30,000 Consider the cost of capital of the two projects is 10%. Copute NPV for both projects and advice the copany. Copute the Internal Rate of Return of both projects. 23. A client has agreed to invest Rs. 100,000 one year fro now in a business planning to expand, and she has decided to set aside the funds today in a bank account proising to pay 7 percent copounded quarterly. How uch does she need to set aside? 24. You have been depositing Rs. 6,000 at the end of every quarter for the last 10 years in a bank which pays 12% interest. Find the aount available at the end of the 10 th year. 25. Rs 1,200 is invested at the beginning of every onth in a deposit account for 10 years at 12%. What is the value of the investent at the end of 10 years. Page 6 of 7

7 26. A couple plans to set aside Rs. 20,000 per year in a conservative portfolio projected to earn 7 percent per year. If they ake their first savings contribution end of the year, how uch will they have at the end of 20 years? 27. A clients plan to send a child a college for four years starting 18 years fro now. Having set aside oney for tuition, she decides to plan for roo and board also. She estiates total costs of Rs. 200,000 by the tie child goes to college. If she starts next year and akes 17 payents in to a savings account paying 10 percent annually, what annual payents ust she ake? 28. Saan, at the age of 32, decided to invest in an annuity. He will put aside Rs sei-annually. a) How uch will he have at the age of 65 if his rate of return is assued to be 10% p.a.? b) If Saan had begun his annuity at the age of 22 instead of 32, what would his annuity be worth at the age of 65? 29. How long does it take to save Rs if you deposit R500 per onth in an account paying 7,5% p.a., copounded onthly? 30. The Board of Investent takes out a bond of Rs to build a new school. The Board is required to ake payents every 6 onths into a sinking fund paying 8% interest per annu copounded sei-annually. At the end of 12 years the Board obligation will be retired. What should the payent at the end of each period be? Page 7 of 7