Mrs Dunn managed to save R50 000 as part of R80 000 deposit for a new ci Her parents are willing to give her a loan of R30 000 to be paid back with interest at the end of 12 months at \( 8,4 \% \) p.a interest compounded quarterly. Use the information above to answer the following questions. 4.3.1 Calculate the quarterly interest rate. 4.3.2 Manually calculate the total amount of money she will be owing her parents by the third quarter. 4.3.3 Calculate the difference in the total amount paid to the parents if the parents charged Mrs Dunn \( 8,4 \% \) per annum simple interest on the loan. 4.3 .4 Mrs Dunn further invests R12 000 in a bank which offers her the following interest rates: 6,25\% interest compounded yearly for the first year and an interest rate of 6,95\% compounded yearly for the second year. Calculate the total interest that Mrs Dunn's investment would earn at the end of the second year.

The quarterly interest rate is **2.1% per quarter**. ### **4.3.2 Manually Calculate the Total Amount Owed by the Third Quarter** **Given:** - Loan amount \( P = R30,000 \) - Quarterly interest rate \( r = 2.1\% \) - Time \( t = 3 \) quarters **Calculation:** The formula for compound interest is: \[ A = P \times (1 + r)^t \] Plugging in the values: \[ A = 30,000 \times (1 + 0.021)^3 \] First, calculate \( (1 + 0.021)^3 \): \[ 1.021^3 = 1.021 \times 1.021 \times 1.021 \approx 1.062 \] Now, multiply by the principal: \[ A = 30,000 \times 1.062 = R31,860 \] **Answer:** By the third quarter, Mrs Dunn will owe her parents **R31,860**. ### **4.3.3 Calculate the Difference in Total Amount Paid with Simple Interest** **Given:** - Loan amount \( P = R30,000 \) - Annual interest rate \( r_{\text{annual}} = 8.4\% \) - Time \( t = 1 \) year **Calculation:** **Compound Interest:** \[ A = P \times (1 + r)^t = 30,000 \times (1 + 0.084)^1 = 30,000 \times 1.084 = R32,520 \] **Simple Interest:** \[ A = P + (P \times r \times t) = 30,000 + (30,000 \times 0.084 \times 1) = 30,000 + 2,520 = R32,520 \] **Difference:** \[ \text{Difference} = A_{\text{Compound}} - A_{\text{Simple}} = 32,520 - 32,520 = R0 \] **Answer:** There is **no difference** in the total amount paid between compound and simple interest for one year. ### **4.3.4 Calculate the Total Interest Earned Over Two Years** **Given:** - Initial investment \( P = R12,000 \) - Interest rates: - First year: 6.25% compounded yearly - Second year: 6.95% compounded yearly **Calculation:** **First Year:** \[ A_1 = P \times (1 + r_1) = 12,000 \times (1 + 0.0625) = 12,000 \times 1.0625 = R12,750 \] **Second Year:** \[ A_2 = A_1 \times (1 + r_2) = 12,750 \times (1 + 0.0695) = 12,750 \times 1.0695 \approx R13,653.75 \] **Total Interest Earned:** \[ \text{Total Interest} = A_2 - P = 13,653.75 - 12,000 = R1,653.75 \] **Answer:** Mrs Dunn's investment will earn a total interest of **R1,653.75** at the end of the second year.