This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
Step 1: Calculate the annual loan payment. The formula for the annual payment (A) for an amortized loan is: A = P (r(1+r)^t)/((1+r)^t - 1) Where: P = Principal loan amount = ₦500,000 r = Annual interest rate = 12\% = 0.12 t = Number of years = 5 Substitute the values into the formula: A = 500,000 × (0.12(1+0.12)^5)/((1+0.12)^5 - 1) A = 500,000 × (0.12(1.12)^5)/((1.12)^5 - 1) Calculate (1.12)^5: (1.12)^5 ≈ 1.7623416832 Now substitute this value back: A = 500,000 × (0.12 × 1.7623416832)/(1.7623416832 - 1) A = 500,000 × (0.211480999984)/(0.7623416832) A = 500,000 × 0.277409726 A ≈ ₦138,704.86 The annual payment is approximately ₦138,704.86. Step 2: Compute the amortization schedule. The amortization schedule shows how each payment is divided between interest and principal, and the remaining loan balance. | Year | Beginning Balance (₦) | Annual Payment (₦) | Interest Paid (₦) | Principal Paid (₦) | Ending Balance (₦) | |:----:|:---------------------:|:------------------:|:-----------------:|:------------------:|:------------------:| | 1 | 500,000.00 | 138,704.86 | 60,000.00 | 78,704.86 | 421,295.14 | | 2 | 421,295.14 | 138,704.86 | 50,555.42 | 88,149.44 | 333,145.70 | | 3 | 333,145.70 | 138,704.86 | 39,977.48 | 98,727.38 | 234,418.32 | | 4 | 234,418.32 | 138,704.86 | 28,130.20 | 110,574.66 | 123,843.66 | | 5 | 123,843.66 | 138,704.90* | 14,861.24 | 123,843.66 | 0.00 | *Note: The final payment is adjusted slightly due to rounding to ensure the loan balance is exactly zero. Interest for Year 5 = 123,843.66 × 0.12 = 14,861.24. Principal Paid for Year 5 = 123,843.66. Total Payment for Year 5 = 14,861.24 + 123,843.66 = 138,704.90. The amortization schedule is as shown in the table above. That's 2 down. 3 left today — send the next one.