SOLVING PROBLEMS: FINANCE Joshua takes out a loan to buy a new lounge suite. The lounge suite costs R 7900 , and interest on the loan is \( 11 \% \) compound interest per year. If Joshua repays the loan in a lump sum afte 4 years, how much must he pay?

To solve this problem, we can use the formula for compound interest: \[ A = P(1 + r)^n \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (initial amount borrowed). - \( r \) is the annual interest rate (in decimal form). - \( n \) is the number of years the money is borrowed for. Given: - The lounge suite costs R 7900. - The interest rate is 11% per year. - Joshua repays the loan in a lump sum after 4 years. We need to find the total amount Joshua must pay after 4 years. Let's calculate the total amount using the compound interest formula. Calculate the value by following steps: - step0: Calculate: \(7900\left(1+0.11\right)^{4}\) - step1: Add the numbers: \(7900\times 1.11^{4}\) - step2: Convert the expressions: \(7900\left(\frac{111}{100}\right)^{4}\) - step3: Simplify: \(7900\times \frac{111^{4}}{100^{4}}\) - step4: Rewrite the expression: \(100\times 79\times \frac{111^{4}}{100^{4}}\) - step5: Reduce the numbers: \(79\times \frac{111^{4}}{100^{3}}\) - step6: Multiply: \(\frac{79\times 111^{4}}{100^{3}}\) The total amount Joshua must pay after 4 years is approximately R 11992.76. Therefore, Joshua must pay R 11992.76 to repay the loan in a lump sum after 4 years.