the car depreciates at \(\text{6}\%\) p.a. straightline depreciation.
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End of chapter exercises
Thabang buys a Mercedes worth \(\text{R}\,\text{385 000}\) in \(\text{2 007}\). What will the value of the Mercedes be at the end of \(\text{2 013}\) if:
the car depreciates at \(\text{6}\%\) p.a. reducingbalance depreciation.
Greg enters into a \(\text{5}\)year hirepurchase agreement to buy a computer for \(\text{R}\,\text{8 900}\). The interest rate is quoted as \(\text{11}\%\) per annum based on simple interest. Calculate the required monthly payment for this contract.
A computer is purchased for \(\text{R}\,\text{16 000}\). It depreciates at \(\text{15}\%\) per annum.
Determine the book value of the computer after \(\text{3}\) years if depreciation is calculated according to the straightline method.
Find the rate according to the reducingbalance method that would yield, after \(\text{3}\) years, the same book value as calculated in the previous question.
Maggie invests \(\text{R}\,\text{12 500}\) for \(\text{5}\) years at \(\text{12}\%\) per annum compounded monthly for the first \(\text{2}\) years and \(\text{14}\%\) per annum compounded semiannually for the next \(\text{3}\) years. How much will Maggie receive in total after \(\text{5}\) years?
Tintin invests \(\text{R}\,\text{120 000}\). He is quoted a nominal interest rate of \(\text{7,2}\%\) per annum compounded monthly.
Calculate the effective rate per annum (correct to two decimal places).
Use the effective rate to calculate the value of Tintin's investment if he invested the money for \(\text{3}\) years.
Suppose Tintin invests his money for a total period of \(\text{4}\) years, but after \(\text{18}\) months makes a withdrawal of \(\text{R}\,\text{20 000}\), how much will he receive at the end of the \(\text{4}\) years?
Ntombi opens accounts at a number of clothing stores and spends freely. She gets herself into terrible debt and she cannot pay off her accounts. She owes Fashion World \(\text{R}\,\text{5 000}\) and the shop agrees to let her pay the bill at a nominal interest rate of \(\text{24}\%\) compounded monthly.
How much money will she owe Fashion World after two years?
What is the effective rate of interest that Fashion World is charging her?
John invests \(\text{R}\,\text{30 000}\) in the bank for a period of \(\text{18}\) months. Calculate how much money he will have at the end of the period and the effective annual interest rate if the nominal interest of \(\text{8}\%\) is compounded:
Calculation  Accumulated amount  Effective annual interest rate  
yearly  
halfyearly  
quarterly  
monthly  
daily 
Calculation  Accumulated amount  Effective annual interest rate  
yearly  \(\text{30 000} \left( 1 + \text{0,08} \right)^{1}\)  \(\text{R}\,\text{33 671,07}\)  
halfyearly  \(\text{30 000} \left( 1 + \frac{\text{0,08}}{2} \right)^{\text{1,5} \times 2}\)  \(\text{R}\,\text{33 745,92}\)  \(\left( 1 + \frac{\text{0,08}}{2} \right)^{2}  1 = \text{8,16}\%\) 
quarterly  \(\text{30 000} \left( 1 + \frac{\text{0,08}}{4} \right)^{\text{1,5} \times 4}\)  \(\text{R}\,\text{33 784,87}\)  \(\left( 1 + \frac{\text{0,08}}{4} \right)^{4}  1 = \text{8,24}\%\) 
monthly  \(\text{30 000} \left( 1 + \frac{\text{0,08}}{12} \right)^{\text{1,5} \times 12}\)  \(\text{R}\,\text{33 811,44}\)  \(\left( 1 + \frac{\text{0,08}}{12} \right)^{12}  1 = \text{8,30}\%\) 
daily  \(\text{30 000} \left( 1 + \frac{\text{0,08}}{\text{365}} \right)^{\text{1,5} \times \text{365}}\)  \(\text{R}\,\text{33 828,17}\)  \(\left( 1 + \frac{\text{0,08}}{\text{365}} \right)^{\text{365}}  1 = \text{8,33}\%\) 
Convert an effective annual interest rate of \(\text{11,6}\%\) p.a. to a nominal interest rate compounded:
Joseph must sell his plot on the West Coast and he needs to get \(\text{R}\,\text{300 000}\) on the sale of the land. If the estate agent charges him \(\text{7}\%\) commission on the selling price, what must the buyer pay for the plot?
Mrs. Brown retired and received a lump sum of \(\text{R}\,\text{200 000}\). She deposited the money in a fixed deposit savings account for \(\text{6}\) years. At the end of the \(\text{6}\) years the value of the investment was \(\text{R}\,\text{265 000}\). If the interest on her investment was compounded monthly, determine:
\(\text{R}\,\text{145 000}\) is invested in an account which offers interest at \(\text{9}\%\) p.a. compounded halfyearly for the first \(\text{2}\) years. Then the interest rate changes to \(\text{4}\%\) p.a. compounded quarterly. Four years after the initial investment, \(\text{R}\,\text{20 000}\) is withdrawn. \(\text{6}\) years after the initial investment, a deposit of \(\text{R}\,\text{15 000}\) is made. Determine the balance of the account at the end of \(\text{8}\) years.
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