8 If N12 000 is invested for 3 yrs at 52 % per annum (a) Find the simple interest (b) Find the total amount at the end of this period. 9 Find how long it would take for an invested sum of N20 000 to generate simple inter est of N5000 at 5% per annum. A photocopier costing N150 000 depreci ates by 5% in the first year, 10% in the sec ond year and 15% in the third year. What is its value after 3 years? 11 A car was bought in 1997 for N550 000 and its value depreciated at the rate of 20% per annum. Calculate the value of the car in 2000. 12 Andrew bought a computer costing N150 000. How much will the same com puter cost in 3 years time if the rate of in flation is 12% per annum? 13 If the rate of inflation is 15% per annum, how long will it take for the price of an item to double? 14 In a shop, washing soap of the same type are sold in three sizes: small: 120 ml at N80 medium: 190 ml at N120 large: 550 ml at N300 Which size is the best to buy and why? A 650 g box of cherio is sold for N300 and a 480 g box is sold for N200. Which one is cheaper to buy and why? 16 Find the cost price or selling price in each of the following: (a) Selling price = N5000, profit = 10% (b) Selling price = N4000, profit = 12% (c) Cost price = N5500, loss = 15% (d) Cost price = N8500, loss = 8% A trader bought an item for N50 000 and sold it at a profit of 12.5%. How much did. she sell the item?
Answers
Answer:
9.2 Simple interest (EMA6M)
Simple interest
Simple interest is interest calculated only on the initial amount that you invested.
As an easy example of simple interest, consider how much we will get by investing R1 000R1 000 for 11 year with a bank that pays 5%5% p.a. simple interest.
At the end of the year we have
Interest=R1 000×5%=R1 000×5100=R1 000×0,05=R50Interest=R1 000×5%=R1 000×5100=R1 000×0,05=R50
With an opening balance of R1 000R1 000 at the start of the year, the closing balance at the end of the year will therefore be
Closing balance=Opening balance + Interest=R1 000+R50=R1 050Closing balance=Opening balance + Interest=R1 000+R50=R1 050
The opening balance in financial calculations is often called the principal, denoted as PP (R1 000R1 000 in the example). The interest rate is usually labelled ii (5%5% p.a. in the example and “p.a.” means per annum or per year). The interest amount is labelled II (R50R50 in the example).
So we can see that
I=P×iI=P×i
and
Closing balance = Opening balance + Interest=P+I=P+P×i=P(1+i)Closing balance = Opening balance + Interest=P+I=P+P×i=P(1+i)
The above calculations give a good idea of what the simple interest formula looks like. However, the example shows an investment that lasts for only one year. If the investment or loan is over a longer period, we need to take this into account. We use the symbol nn to indicate time period, which must be given in years.
The general formula for calculating simple interest is