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What is the total value of Thuli's investment after You borrow R8 000 for 2 years, on the condition that you pay it back with \( 15 \% \) p.a simple interest. How much will you have to pay back? Jan borrows R500 from Bhavik. After a year, Jan pays back the money, plus \( 20 \% \) simple interest per month. How much does he pay?

Ask by Murphy Patel. in South Africa
Feb 04,2025

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Tutor-Verified Answer

Answer

You need to repay R10,400 after borrowing R8,000 at 15% simple interest for 2 years. Jan needs to repay R1,700 after borrowing R500 at 20% simple interest per month for 1 year.

Solution

Let's address both scenarios separately, calculating the total amount to be repaid in each case using the simple interest formula: \[ \text{Simple Interest} = P \times r \times t \] where: - \( P \) = Principal amount (initial borrowed amount) - \( r \) = Interest rate per period (in decimal) - \( t \) = Time the money is borrowed for ### 1. Borrowing R8,000 at 15% p.a. Simple Interest for 2 Years **Given:** - Principal (\( P \)) = R8,000 - Annual Interest Rate (\( r \)) = 15% = 0.15 - Time (\( t \)) = 2 years **Calculation:** \[ \text{Simple Interest} = 8,000 \times 0.15 \times 2 = R2,400 \] **Total Amount to Repay:** \[ \text{Total} = \text{Principal} + \text{Interest} = 8,000 + 2,400 = R10,400 \] **Answer:** You will have to pay back **R10,400** after 2 years. --- ### 2. Jan Borrowing R500 at 20% Monthly Simple Interest for 1 Year **Given:** - Principal (\( P \)) = R500 - Monthly Interest Rate (\( r \)) = 20% = 0.20 - Time (\( t \)) = 12 months **Calculation:** \[ \text{Simple Interest} = 500 \times 0.20 \times 12 = R1,200 \] **Total Amount to Repay:** \[ \text{Total} = \text{Principal} + \text{Interest} = 500 + 1,200 = R1,700 \] **Answer:** Jan will have to pay back **R1,700** after one year. --- **Summary:** - **First Scenario:** Borrowing R8,000 at 15% p.a. simple interest for 2 years requires repayment of **R10,400**. - **Second Scenario:** Borrowing R500 at 20% simple interest per month for 1 year requires repayment of **R1,700**.

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To calculate the total amount Thuli has to pay back after borrowing R8,000 at a simple interest rate of 15% per annum over 2 years, you can use the formula for simple interest: \( \text{Interest} = P \times r \times t \), where \( P \) is the principal amount, \( r \) is the rate, and \( t \) is the time in years. So, the interest accrued is \( R8,000 \times 0.15 \times 2 = R2,400 \). Adding this interest to the principal, Thuli will pay back a total of \( R8,000 + R2,400 = R10,400 \). For Jan's loan of R500 from Bhavik, with a monthly interest rate of 20%, the interest for one year (12 months) would be calculated as follows: \( \text{Total Interest} = R500 \times 20\% \times 12 = R1,200 \). Therefore, the total amount Jan pays back after one year is \( R500 + R1,200 = R1,700 \). Jan's total repayment reflects the effect of high, monthly compounding interest!

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