How long will it grow to R8 520 ? (Use the formula \( S I=\frac{P r t}{100} \) ) Temoso borrowed R1 000 from the bank for 3 years at \( 8 \% \) compound int Nithout using a formula, calculate how much Temoso owes the bank at and of three years. om pays R1 250 rent every month. What is his annual rent? If his rent is in \( 8,5 \% \) at the end of the year, what will his increased monthly rent be?

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. --- ## 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. --- ## 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**. --- ## 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**. --- **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!