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Sagot :
Certainly! Let's break down the solution step-by-step for each sub-question.
### 1.1.1 Calculate how much Tumi would be able to invest with the bank, if he invests the entire amount.
Tumi starts saving R800 per month for 2 years (24 months).
1. Determine the total savings over the period:
[tex]\[ \text{Total Savings} = \text{Monthly Savings} \times \text{Number of Months} \][/tex]
[tex]\[ \text{Total Savings} = 800 \, \text{R/month} \times 24 \, \text{months} \][/tex]
Result:
[tex]\[ \text{Total Savings} = 19,200 \, \text{R} \][/tex]
So, Tumi would be able to invest R19,200 with the bank.
### 1.1.2 Calculate the interest earned in this period.
The bank offers an annual simple interest rate of [tex]\(12.5\%\)[/tex] over a period of 36 months (3 years).
1. Convert the percentage to a decimal:
[tex]\[ \text{Interest Rate} = \frac{12.5}{100} = 0.125 \][/tex]
2. Convert months to years for the investment period:
[tex]\[ \text{Investment Period (Years)} = \frac{36 \, \text{months}}{12 \, \text{months/year}} = 3 \, \text{years} \][/tex]
3. Calculate the interest earned using the formula for simple interest:
[tex]\[ \text{Interest Earned} = \text{Principal} \times \text{Interest Rate} \times \text{Time (Years)} \][/tex]
[tex]\[ \text{Interest Earned} = 19,200 \, \text{R} \times 0.125 \times 3 \, \text{years} \][/tex]
Result:
[tex]\[ \text{Interest Earned} = 7,200 \, \text{R} \][/tex]
So, the interest earned in this period is R7,200.
### 1.1.3 What is the total amount that he will receive at the end of the investment period?
1. Calculate the total amount received:
[tex]\[ \text{Total Amount Received} = \text{Principal} + \text{Interest Earned} \][/tex]
[tex]\[ \text{Total Amount Received} = 19,200 \, \text{R} + 7,200 \, \text{R} \][/tex]
Result:
[tex]\[ \text{Total Amount Received} = 26,400 \, \text{R} \][/tex]
So, the total amount that Tumi will receive at the end of the investment period is R26,400.
### Summary:
1. Amount Tumi will invest: R19,200
2. Interest earned in 36 months: R7,200
3. Total amount received at the end of the investment period: R26,400
### 1.1.1 Calculate how much Tumi would be able to invest with the bank, if he invests the entire amount.
Tumi starts saving R800 per month for 2 years (24 months).
1. Determine the total savings over the period:
[tex]\[ \text{Total Savings} = \text{Monthly Savings} \times \text{Number of Months} \][/tex]
[tex]\[ \text{Total Savings} = 800 \, \text{R/month} \times 24 \, \text{months} \][/tex]
Result:
[tex]\[ \text{Total Savings} = 19,200 \, \text{R} \][/tex]
So, Tumi would be able to invest R19,200 with the bank.
### 1.1.2 Calculate the interest earned in this period.
The bank offers an annual simple interest rate of [tex]\(12.5\%\)[/tex] over a period of 36 months (3 years).
1. Convert the percentage to a decimal:
[tex]\[ \text{Interest Rate} = \frac{12.5}{100} = 0.125 \][/tex]
2. Convert months to years for the investment period:
[tex]\[ \text{Investment Period (Years)} = \frac{36 \, \text{months}}{12 \, \text{months/year}} = 3 \, \text{years} \][/tex]
3. Calculate the interest earned using the formula for simple interest:
[tex]\[ \text{Interest Earned} = \text{Principal} \times \text{Interest Rate} \times \text{Time (Years)} \][/tex]
[tex]\[ \text{Interest Earned} = 19,200 \, \text{R} \times 0.125 \times 3 \, \text{years} \][/tex]
Result:
[tex]\[ \text{Interest Earned} = 7,200 \, \text{R} \][/tex]
So, the interest earned in this period is R7,200.
### 1.1.3 What is the total amount that he will receive at the end of the investment period?
1. Calculate the total amount received:
[tex]\[ \text{Total Amount Received} = \text{Principal} + \text{Interest Earned} \][/tex]
[tex]\[ \text{Total Amount Received} = 19,200 \, \text{R} + 7,200 \, \text{R} \][/tex]
Result:
[tex]\[ \text{Total Amount Received} = 26,400 \, \text{R} \][/tex]
So, the total amount that Tumi will receive at the end of the investment period is R26,400.
### Summary:
1. Amount Tumi will invest: R19,200
2. Interest earned in 36 months: R7,200
3. Total amount received at the end of the investment period: R26,400
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