ANNUITIES AND AMORTISATION WORKSHOP
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1 OBJECTIVE: 1. Able to calculate the present value of annuities 2. Able to calculate the future value of annuities 3. Able to complete an amortisation schedule TARGET: QMI1500 and BNU1501, any other modules using Annuities and amortisation. ANNUITIES Present Value Future Value An annuity is A series of constant payments That occur at regular intervals and Do not continue forever. NOTE: The first payment occurs next period (not now). The constant cash flows of a 3-year annuity of R per year at 10% can be represented on a time line: Compiled by EM Booi Parowstatisticstutor@gmail.com Page 1
2 Present Value of an Annuity Borrowing Problems (Loans) How much can I borrow (PV / P)? How much are my payments (PMT / R)? What interest rate am I getting (I/Y / i)? How long will it take (N / n)? Future Value of an Annuity Savings Problems (Retirement Fund) How much will I have (FV / S)? How much are my payments (PMT / R)? What interest rate am I getting (I/Y / i)? How long will it take (N / n)? Compiled by EM Booi Parowstatisticstutor@gmail.com Page 2
3 Using Financial Calculator EXERCISE: Future Value of an Annuity How much will you have if you save R per year for 25 years at 8%? R7, Compiled by EM Booi Page 3
4 How much will you have if you save R per year for 5 years at 7%? R5, How much will you have if you save R1.00 per year for 50 years at 10%? R1, Present Value of an Annuity What is the present value of R per year for 25 years at 8%? R1, What is the present value of R per year for 5 years at 7%? R4, What is the present value of R1.00 per year for 50 years at 10%? R9.91 Compiled by EM Booi Parowstatisticstutor@gmail.com Page 4
5 Amortisation is: a simple way to evenly spread out costs over a period of time. we amortize items such as loans, rent /mortgages, annual subscriptions and intangible assets. Amortisation schedule is a table indicating the distribution of each payment in regard to interest and principal reduction Compiled by EM Booi Parowstatisticstutor@gmail.com Page 5
6 (a) Payment: R = P [ (1+i)n 1 i(1+i)n ] (b) Interest: I = PRT (c) Principal repaid: principal repaid = payment interest due (d) Outstanding Principal: OP = outstanding principal from previous year principal repaid from previous year EXAMPLE Draw up an amortisation schedule for a loan of R4 000 for three years at 15% per annum compounded halfyearly and repayable in six half-year payments Compiled by EM Booi Parowstatisticstutor@gmail.com Page 6
7 Using Financial Calculator: Compiled by EM Booi Page 7
8 Exercise1: EXERCISES: Exercise2: Compiled by EM Booi Page 8
9 Exercise3: Exercise4: Exercise5: Compiled by EM Booi Page 9
10 Exercise6: Exercise7: Compiled by EM Booi Page 10
11 Exercise8: Compiled by EM Booi Page 11
12 Exercise9: Exercise10: Exercise11: References: 1. QMI1500 & BNU1501 Study guide and tutorial letters 2. QMI1500 & BNU1501 Past Exam papers Compiled by EM Booi Page 12
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