FINANCE, GROWTH & DECAY (LIVE) 08 APRIL 2015 Section A: Summary Notes and Examples There are two types of formula dealt with in this section: Future Value Annuity Formula where: equal and regular payment per period number of payments interest rate as a decimal This formula deals with saving money for the future. Remember that the value of of payments and not necessarily the duration of the investment. Use the future value formula when working with: 1. Retirement annuities 2. Savings accounts 3. Sinking funds Sinking Funds represents the number Vehicles, equipment, machinery and other similar assets, all depreciate in value as a result of usage and age. Businesses often set aside money for replacing outdated equipment or old vehicles in accounts called sinking funds. Regular deposits, and sometimes lump sum deposits, are made into these accounts so that enough money will have accumulated by the time a new machine or vehicle needs to be purchased. Present Value Annuity Formula where: equal and regular payment per period number of payments interest rate as a decimal Use the present value formula when working with: 1. Repayments of home loans 2. Hire-purchase agreements 3. Student loans Section B: Practice Questions Question 1 Thembile invests R 3500 into a savings account which pays 7,5% per annum compounded yearly. After an unknown period of time his account is worth R 4044,69. For how long did Thembile invest his money? Page 1
Question 2 Convert an effective rate of 12,5% per annum, to a nominal rate per annum compounded half yearly. Question 3 Ciza decides to start saving money for the future. At the end of each month she deposits R 900 into an account at Harringstone Mutual Bank, which earns 8,25% interest p.a. compounded monthly. a) Determine the balance of Ciza s account after 29 years. b) How much money did Ciza deposit into her account over the 29 period? c) Calculate how much interest she earned over the 29 period. Question 4 Kosma is planning a trip to Canada to visit her friend in two years time. She makes an itinerary for her holiday and expects that the trip will cost R 25 000. How much must she save at the end of every month if her savings account earns an interest of 10,7% per annum compounded monthly? Question 5 Wellington Courier Company buys a delivery truck for R 296 000. The value of the truck depreciates on a reducing-balance at 18% per annum. The company plans to replace this truck in seven years time. a) Calculate the book value of the delivery truck in seven years time. b) Determine the minimum balance of the sinking fund in order for the company to afford a new truck in seven years time. The price of trucks is estimated to increase at 9% per annum each year. c) Calculate the required monthly deposits if the sinking fund earns an interest rate of 13% per annum compounded. Question 6 Andre takes out a student loan for his first year of civil engineering. The loan agreement states that the repayment period is equal to 1,5 year for every year of financial assistance granted and that the loan is subject to an interest rate of 10,5% p.a. compounded monthly. a) If Andre pays a monthly installment of R 1446,91, calculate the loan amount. b) Determine how much interest Andre will have paid on his student loan at the end of the 18 months. Section C: Solutions Question 1 Step 1: Write down the compound interest formula and the known values. Step 2: Substitute the values and solve for Page 2
Step 3: Write final answer. The R 3500 was invested for 2 years. Page 3
Question 3 Step 1: Write down the given information and the future value formula Step 2: Substitute the known values and use a calculator to determine F. Remember: do not round off any of the interim steps of a calculation as this will affect the accuracy of the final answer. Step 3: Calculate the total value of deposits into the account. Ciza deposited R 900 each month for 29 years. Step 4: Calculate the total interest earned Question 4 Step 1: Write down the given information and the future value formula. To determine the monthly payment amount, we make the subject of the formula: Step 2: Substitute the known values and calculate. Step 3: Write the final answer. Kosma must save R 938,80 each month so that she can afford her holiday. Page 4
Question 5 Step 1: Determine the book value of the truck in seven years time. Step 2: Determine the minimum balance of the sinking fund. Calculate the price of a new truck in seven years time. Therefore, the balance of the sinking fund must be greater than the cost of a new truck in seven years time minus the money from the sale of the old truck. Step 3: Calculate the required monthly payment into the sinking fund. Substitute the values and calculate. Therefore, the company must deposit R 348,77 each month. Page 5
Question 6 Step 1: Write down the given information and the present value formula. Substitute the known values and determine : Therefore, Andre took out a student loan for R 24 000. Step 2: Calculate the total amount of interest. At the end of the 18 month period: Page 6