How many years will it take for 136000dollars to grow to be 468000dollars if it is invested in account with an annual interest rate of 80%
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.