We appreciate your visit to ACTIVITY 2 Josli saved R300 00 each month since earning his first profit He has now accumulated an amount of R17 000 00 TABLE 2. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Below is a detailed step-by-step solution for the question.
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Step 2.1 – Determine the Time in Months to Save R17000.00
Josli saves a fixed amount of R300.00 each month. His total accumulated savings is R17000.00. To find the number of months required, we use the formula
[tex]$$
\text{Number of months} = \frac{\text{Total Savings}}{\text{Monthly Savings}}.
$$[/tex]
Substitute the values:
[tex]$$
\text{Number of months} = \frac{17000}{300} \approx 56.67.
$$[/tex]
Since savings are made in whole months, Josli must complete a full month of saving. Therefore, he needed to save for
[tex]$$
57 \text{ months.}
$$[/tex]
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Step 2.2 – Determine the Interest Rate for a 3-year Investment
For an investment period of 3 years (which is equivalent to 36 months) and for an amount in the range R10,000.00 to R24,999.00, the table indicates that the annual simple interest rate is
[tex]$$
8.08\% \text{ per year.}
$$[/tex]
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Step 2.3 – Calculate the Interest Earned (Rounded to the Nearest R100)
The simple interest formula is given by
[tex]$$
I = P \cdot \frac{r}{100} \cdot t,
$$[/tex]
where:
- [tex]$P$[/tex] is the principal amount (R17000.00),
- [tex]$r$[/tex] is the annual interest rate (8.08%), and
- [tex]$t$[/tex] is the time in years (3 years).
Substitute the given values:
[tex]$$
I = 17000 \times \frac{8.08}{100} \times 3 \approx 17000 \times 0.0808 \times 3 \approx 4120.8.
$$[/tex]
Rounded to the nearest R100, the interest is
[tex]$$
\text{Interest} \approx R4100.
$$[/tex]
──────────────────────────────
Step 2.4 – Calculate the Difference in Interest Rate for Sifiso’s Investment
Sifiso wants to invest R24000.00 for different periods. For amounts between R10,000.00 and R24,999.00, the interest rates are:
- 12 months: [tex]$7.12\%$[/tex] per year,
- 48 months: [tex]$8.30\%$[/tex] per year.
The difference in the interest rates, in percentage points, is
[tex]$$
8.30\% - 7.12\% = 1.18 \text{ percentage points.}
$$[/tex]
──────────────────────────────
Step 2.5 – Minimum Time Required for an Interest Rate of [tex]$8.41\%$[/tex] for an Investment of R25000.00
For amounts between R25,000.00 and R99,999.00, the table shows that an interest rate of [tex]$8.41\%$[/tex] per year is available for an investment term of 24 months.
Convert 24 months into years:
[tex]$$
\text{Years} = \frac{24}{12} = 2 \text{ years},
$$[/tex]
with no additional months remaining.
──────────────────────────────
Final Answers:
2.1 Josli took 57 months to save R17000.00.
2.2 The interest rate for a 3-year investment is [tex]$8.08\%$[/tex] per year.
2.3 The interest earned over 3 years is approximately R4100.
2.4 The difference in interest rate for 48 months compared to 12 months is [tex]$1.18$[/tex] percentage points.
2.5 The minimum investment period for an interest rate of [tex]$8.41\%$[/tex] is 2 years (or 2 years and 0 months).
──────────────────────────────
Step 2.1 – Determine the Time in Months to Save R17000.00
Josli saves a fixed amount of R300.00 each month. His total accumulated savings is R17000.00. To find the number of months required, we use the formula
[tex]$$
\text{Number of months} = \frac{\text{Total Savings}}{\text{Monthly Savings}}.
$$[/tex]
Substitute the values:
[tex]$$
\text{Number of months} = \frac{17000}{300} \approx 56.67.
$$[/tex]
Since savings are made in whole months, Josli must complete a full month of saving. Therefore, he needed to save for
[tex]$$
57 \text{ months.}
$$[/tex]
──────────────────────────────
Step 2.2 – Determine the Interest Rate for a 3-year Investment
For an investment period of 3 years (which is equivalent to 36 months) and for an amount in the range R10,000.00 to R24,999.00, the table indicates that the annual simple interest rate is
[tex]$$
8.08\% \text{ per year.}
$$[/tex]
──────────────────────────────
Step 2.3 – Calculate the Interest Earned (Rounded to the Nearest R100)
The simple interest formula is given by
[tex]$$
I = P \cdot \frac{r}{100} \cdot t,
$$[/tex]
where:
- [tex]$P$[/tex] is the principal amount (R17000.00),
- [tex]$r$[/tex] is the annual interest rate (8.08%), and
- [tex]$t$[/tex] is the time in years (3 years).
Substitute the given values:
[tex]$$
I = 17000 \times \frac{8.08}{100} \times 3 \approx 17000 \times 0.0808 \times 3 \approx 4120.8.
$$[/tex]
Rounded to the nearest R100, the interest is
[tex]$$
\text{Interest} \approx R4100.
$$[/tex]
──────────────────────────────
Step 2.4 – Calculate the Difference in Interest Rate for Sifiso’s Investment
Sifiso wants to invest R24000.00 for different periods. For amounts between R10,000.00 and R24,999.00, the interest rates are:
- 12 months: [tex]$7.12\%$[/tex] per year,
- 48 months: [tex]$8.30\%$[/tex] per year.
The difference in the interest rates, in percentage points, is
[tex]$$
8.30\% - 7.12\% = 1.18 \text{ percentage points.}
$$[/tex]
──────────────────────────────
Step 2.5 – Minimum Time Required for an Interest Rate of [tex]$8.41\%$[/tex] for an Investment of R25000.00
For amounts between R25,000.00 and R99,999.00, the table shows that an interest rate of [tex]$8.41\%$[/tex] per year is available for an investment term of 24 months.
Convert 24 months into years:
[tex]$$
\text{Years} = \frac{24}{12} = 2 \text{ years},
$$[/tex]
with no additional months remaining.
──────────────────────────────
Final Answers:
2.1 Josli took 57 months to save R17000.00.
2.2 The interest rate for a 3-year investment is [tex]$8.08\%$[/tex] per year.
2.3 The interest earned over 3 years is approximately R4100.
2.4 The difference in interest rate for 48 months compared to 12 months is [tex]$1.18$[/tex] percentage points.
2.5 The minimum investment period for an interest rate of [tex]$8.41\%$[/tex] is 2 years (or 2 years and 0 months).
Thanks for taking the time to read ACTIVITY 2 Josli saved R300 00 each month since earning his first profit He has now accumulated an amount of R17 000 00 TABLE 2. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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