Chapter 5 more about interest edulink
0 likes164 views
1. The document discusses concepts related to depreciation, inflation, and nominal and effective interest rates. It provides terminology, formulas, and examples to explain these concepts. 2. Depreciation refers to how assets decrease in value over time. Inflation refers to rising prices over time which reduces purchasing power. Nominal interest rates do not account for inflation while effective rates factor in compounding periods. 3. Examples are given to demonstrate calculating depreciation using straight-line and reducing balance methods, accounting for inflation, and comparing nominal to effective interest rates when interest is compounded more frequently.
Chapter 5 more about interest edulink
- 1. 2013/04/17 1 MORE ABOUT INTEREST X-Kit Textbook Chapter 5 CONTENT Depreciation Inflation Nominal & Effective Interest Rates CONTENT- QUESTIONS How our belongings decrease in value over time? How much our money buys us over time? How much is our money worth? EXAMPLE For his construction business, Jim’s father bought a car 5 years ago for R50 000. Now, he wants to sell the vehicle. But the car is now only worth R20 000. We call this DEPRECIATION. TERMINOLOGY Term Explanation Assets Things we own that are valuable or useful, like a car or laptop. Book Value The original cost of an asset less the depreciation. Scrap Value The Book Value at the end of an asset’s life. Straight line Depreciation Subtract equal amounts every year from the purchase price of an asset. Spread the depreciation evenly over the life of an asset. Reducing Balance Depreciation Subtract the greatest amount from the present value for the first year and smaller amounts for each year afterwards. DEPRECIATION • Straight Line Depreciation: 𝑭𝑽 = 𝑷𝑽 𝟏 − 𝒊 × 𝒏 • Reducing Balance Depreciation: 𝑭𝑽 = 𝑷𝑽 𝟏 − 𝒊 𝒏 𝐹𝑉 = Future Value / Scrap Value 𝑃𝑉 = Present Value / Original Cost of an asset 𝑖 = Depreciation Rate per year 𝑛 = Number of years
- 2. 2013/04/17 2 EXAMPLE Jim buys a new mountain bike for R5 000. The straight line depreciation rate is 21% per year. What will his mountain bike be worth in 4 years’ time? EXAMPLE Jim’s older brother buys a new 4x4 for R185 000. But, after 6 years, the 4x4 will only be worth R42 000. What is the annual rate of depreciation using straight line depreciation? EXAMPLE It is Jim’s job to mow the lawn at home. Jim’s parents buy a new lawn mower for R1 800. The straight line depreciation rate is 20%. How long will it take for the new lawn mower to be worth R0? In other words, find out when the lawn mower’s scrap value is zero? EXAMPLE Mamphela buys a new car for R80 000. Find the scrap value of the car after 5 years using reducing balance depreciation at 18% per annum? EXAMPLE A bottling machine in a soft-drink factory costs R1 200 000. The factory owner expects that the machine will last for 8 years. After 8 years, its scrap value will be R100 000. Find the annual rate of depreciation using reducing balance depreciation. EXAMPLE A tourism company offers flights in a hot- air balloon. A new hot-air balloon costs R570 000. Depreciation is at 25% p.a. on a reducing balance. After how many years will the hot-air balloon have a value of R50 000?
- 3. 2013/04/17 3 INFLATION • Some things are worth less over time = Depreciation. • The price of things goes up over time = Inflation. • Purchasing power depends on the rate of inflation over the year (for example, invest R1 000 at an 10% interest rate for 1 year, but inflation rate is 10%, you gained nothing). • The effects of inflation can eat up the interest on our investments. • The nominal interest rate is the rate at which an investment increases. • The real interest rate is the rate at which the purchasing power of an investment increases. WORK WITHINFLATION Suppose the inflation rate over the year is 6%. In other words, the prices of goods have gone up, on average, by 6% over the year. So every rand that you spend next year will buy you 6% less. EXAMPLE Find the real future value at an inflation rate of 6%, of an investment of R1 000, invested for 1 year at an 10% annual interest rate. 𝑅𝑒𝑎𝑙 𝐹𝑢𝑡𝑢𝑟𝑒 𝑉𝑎𝑙𝑢𝑒 = 𝐹𝑢𝑡𝑢𝑟𝑒 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 1 + 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑛 • Your R1 100 investment is only worth R1 037,74 in purchasing power. • The nominal payoff on the investment is R1 100. • The Real payoff is R1 037,74 EXAMPLE Cindy and Londi both inherit R500 000. Cindy buys a house for R440 000 and a second-hand car for R60 000. Londi buys a house for R280 000 and a new car for R220 000. The cars depreciate (straight line depreciation) at 10% p.a. The houses appreciate (value increases) at 5% p.a. Whose investment is worth more after 2 years? COMPARISONOF FUTUREVALUES Inheritance of R500 000 Value of assets after 2 years House Car House Car Total Cindy R440 000 R60 000 R485 100 R48 000 R533 100 Londi R280 000 R220 000 R308 700 R176 000 R484 700 EXAMPLE In April 2003 a bank’s cheque account statement included the following as part of the bank’s advertising: “Did you know that university fees (class fees only) will be a staggering R26 000 a year by 2011?” In 2003 Rhodes University’s academic fees were on average R14 500 per year. What annual rate of inflation was the bank using?
- 4. 2013/04/17 4 NOMINAL& EFFECTIVEINTERESTRATES • The nominal interest rate is the percentage rate that the bank will charge for a loan or investment. • The effective interest rate is the rate the customer will pay or receive. How much will depend on how often the bank adds the interest amount to the loan. (Different compounding periods – annual, quarterly, monthly or daily) Jim borrowedR100for 1 year @ 15% p.a. Period Interval per year Formula Future Value Interest Payable Effective Annual Rate Annual 1 100 1 + 0.15 1 1 R115 R15 15% Half- yearly 2 100 1 + 0.15 2 2 R115.56 R15.56 15.56% Monthly 12 100 1 + 0.15 12 12 R116.08 R16.08 16.08% Daily 365 100 1 + 0.15 365 365 R116.18 R16.18 16.18% NOMINAL& EFFECTIVEINTERESTRATES The more often interest is compounded, the higher the effective rate of interest. NOMINAL& EFFECTIVEINTERESTRATES 𝒊 𝒆𝒇𝒇 = 𝟏 + 𝒊 𝒎 𝒎 − 𝟏 • 𝑖 = the nominal (annual) interest rate • 𝑚 = the number of times interest is compounded in a year • 𝑖 𝑒𝑓𝑓 = the effective interest rate EXAMPLE If you save money in an investment account at a nominal rate of 12% compounded monthly, what is the effective rate of interest? EXAMPLE The owners of a fast-food pizza business buy a new delivery vehicle for R80 000. After 5 years, they will have to replace the old bakkie with a new one because old vehicles are expensive to keep going. The business writes off the depreciating value of the vehicle every year at a rate of 12% on a reducing balance. The owners of the business want to know how much they will be able to sell the bakkie for after 5 years. They also want to know how much it will cost to buy the same kind of delivery vehicle in 5 years’ time. Inflation is 14% p.a. Lastly, the owners wants to know how much extra money they will need to buy a new vehicle after selling the old one at its scrap value.
- 5. 2013/04/17 5 STRUCTURETHE QUESTION 1. We want to know the future value (book value/scrap value) of the first vehicle with 12% depreciation. 2. We also want to know the future value of the new vehicle at 14% inflation. 3. Lastly, we want to know the difference between the cost of a new vehicle and the scrap value of the old one.