Choose a language Whole numbers soLVING PROBLEMS: FINANCE Thobeka takes out a loan to buy a new TV. The TV costs R 5600 , and interest on the loan is \( 14 \% \) compound interest per year. If Thobeka repays the loan in a lump sum after 4 years, how much must she pay? INSTRUCTION: Round vour answer to

To find out how much Thobeka must pay to repay the loan in a lump sum after 4 years, we can use the formula for compound interest: \[ A = P(1 + r)^n \] Where: - \( A \) is the amount Thobeka must pay after 4 years, - \( P \) is the principal amount (the cost of the TV, R 5600), - \( r \) is the annual interest rate (14%), - \( n \) is the number of years (4). Substitute the given values into the formula: \[ A = 5600(1 + 0.14)^4 \] Now, we can calculate the amount Thobeka must pay after 4 years. Calculate the value by following steps: - step0: Calculate: \(5600\left(1+0.14\right)^{4}\) - step1: Add the numbers: \(5600\times 1.14^{4}\) - step2: Convert the expressions: \(5600\left(\frac{57}{50}\right)^{4}\) - step3: Simplify: \(5600\times \frac{57^{4}}{50^{4}}\) - step4: Rewrite the expression: \(50\times 112\times \frac{57^{4}}{50^{4}}\) - step5: Reduce the numbers: \(112\times \frac{57^{4}}{50^{3}}\) - step6: Rewrite the expression: \(16\times 7\times \frac{57^{4}}{50^{3}}\) - step7: Rewrite the expression: \(16\times 7\times \frac{57^{4}}{2^{3}\times 25^{3}}\) - step8: Rewrite the expression: \(2^{4}\times 7\times \frac{57^{4}}{2^{3}\times 25^{3}}\) - step9: Reduce the numbers: \(2\times 7\times \frac{57^{4}}{25^{3}}\) - step10: Multiply: \(\frac{14\times 57^{4}}{25^{3}}\) - step11: Simplify: \(\frac{14\times 57^{4}}{15625}\) Thobeka must pay R 9458.18 to repay the loan in a lump sum after 4 years.