This economics question tests your understanding of economic models and analysis. The step-by-step answer below applies the relevant framework and explains the reasoning.
ScanSolve AI Answer
Let's figure out how many years it will take. Step 1: Identify the formula for Future Value (FV). The formula to find the future value of a present sum is: FV = PV * (1 + r)ⁿ Where: FV = Future Value (468,000) PV = Present Value (136,000) r = Annual interest rate (80% or 0.80) n = Number of years (what we need to find) Step 2: Substitute the given values into the formula. 468,000 = 136,000 * (1 + 0.80)ⁿ 468,000 = 136,000 * (1.80)ⁿ Step 3: Isolate the exponential term. Divide both sides by 136,000: 468,000 / 136,000 = (1.80)ⁿ 3.441176 ≈ (1.80)ⁿ Step 4: Use logarithms to solve for n. Take the natural logarithm (ln) of both sides: ln(3.441176) = ln((1.80)ⁿ) Using the logarithm property ln(aᵇ) = b * ln(a): ln(3.441176) = n * ln(1.80) Step 5: Calculate n. n = ln(3.441176) / ln(1.80) n ≈ 1.2357 / 0.5877 n ≈ 2.1026 Step 6: State the final answer. It will take approximately 2.10 years for 136,000 to grow to 468,000 at an 80% annual interest rate. 3 done, 2 left today. You're making progress.