Answer
It will take 94 years for R1,000 to grow to R8,520 at 8% simple interest. After 3 years, Temoso owes R1,259.71 on a R1,000 loan at 8% compound interest. Om's annual rent is R15,000, and after an 8.5% increase, his new monthly rent is R1,356.25.
Solution
It appears you have several financial questions related to simple interest, compound interest, and rent calculations. I'll address each of them step-by-step to ensure clarity.
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## 1. **Simple Interest Calculation: Time to Grow to R8,520**
**Given:**
- **Principal (P):** R1,000
- **Rate of Interest (r):** 8% per annum
- **Total Amount (A):** R8,520
**Formula:**
\[ \text{Simple Interest (SI)} = \frac{P \times r \times t}{100} \]
\[ A = P + SI \]
**Objective:**
Find the time (t) it takes for R1,000 to grow to R8,520 at 8% simple interest.
**Step-by-Step Calculation:**
1. **Express Total Amount in Terms of Simple Interest:**
\[ A = P + \frac{P \times r \times t}{100} \]
\[ 8,520 = 1,000 + \frac{1,000 \times 8 \times t}{100} \]
2. **Simplify the Equation:**
\[ 8,520 = 1,000 + 80t \]
3. **Isolate t:**
\[ 8,520 - 1,000 = 80t \]
\[ 7,520 = 80t \]
\[ t = \frac{7,520}{80} \]
\[ t = 94 \text{ years} \]
**Conclusion:**
At an 8% simple interest rate, it will take **94 years** for R1,000 to grow to R8,520.
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## 2. **Compound Interest Calculation: Amount Owed After 3 Years**
**Given:**
- **Principal (P):** R1,000
- **Rate of Interest (r):** 8% per annum
- **Time (t):** 3 years
- **Interest Type:** Compound Interest (compounded annually)
**Objective:**
Calculate the total amount Temoso owes the bank after 3 years without using the compound interest formula directly.
**Manual Calculation Steps:**
1. **Year 1:**
- **Interest:** 8% of R1,000 = 0.08 × 1,000 = R80
- **Amount at End of Year 1:** R1,000 + R80 = R1,080
2. **Year 2:**
- **Interest:** 8% of R1,080 = 0.08 × 1,080 = R86.40
- **Amount at End of Year 2:** R1,080 + R86.40 = R1,166.40
3. **Year 3:**
- **Interest:** 8% of R1,166.40 = 0.08 × 1,166.40 = R93.31
- **Amount at End of Year 3:** R1,166.40 + R93.31 = R1,259.71
**Conclusion:**
After **3 years**, Temoso will owe the bank **R1,259.71**.
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## 3. **Rent Calculation: Annual Rent and Increased Monthly Rent**
### a. **Calculating Annual Rent**
**Given:**
- **Monthly Rent:** R1,250
**Objective:**
Find the total rent paid annually.
**Calculation:**
\[ \text{Annual Rent} = \text{Monthly Rent} \times 12 \]
\[ \text{Annual Rent} = 1,250 \times 12 = R15,000 \]
**Conclusion:**
Om's **annual rent** is **R15,000**.
### b. **Calculating Increased Monthly Rent After 8.5% Increase**
**Given:**
- **Original Monthly Rent:** R1,250
- **Increase Rate:** 8.5%
**Objective:**
Find the new monthly rent after an 8.5% increase.
**Calculation:**
\[ \text{Increased Monthly Rent} = \text{Original Monthly Rent} \times \left(1 + \frac{8.5}{100}\right) \]
\[ \text{Increased Monthly Rent} = 1,250 \times 1.085 \]
\[ \text{Increased Monthly Rent} = R1,356.25 \]
**Conclusion:**
After an **8.5%** increase, Om's **new monthly rent** will be **R1,356.25**.
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**Summary of Answers:**
1. **Simple Interest:** It will take **94 years** for R1,000 to grow to R8,520 at 8% simple interest.
2. **Compound Interest:** Temoso will owe **R1,259.71** after 3 years on a R1,000 loan at 8% compound interest.
3. **Rent:**
- **Annual Rent:** R15,000
- **Increased Monthly Rent after 8.5% Increase:** R1,356.25
If you have any further questions or need additional clarifications, feel free to ask!
Reviewed and approved by the UpStudy tutoring team
Explain
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