If you wish to accumulate 140,000dollars in 13 years how much you deposit today in an account that pays an annual interest rate of 14%
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 calculate how much you need to deposit today.
Step 1: Identify the formula for Present Value (PV).
The formula to find the present value of a future sum is:
PV = FV / (1 + r)ⁿ
Where:
PV = Present Value (the amount to deposit today)
FV = Future Value ($140,000)
r = Annual interest rate (14% or 0.14)
n = Number of years (13)
Step 2: Substitute the given values into the formula.
PV = 140,000 / (1 + 0.14)¹³
Step 3: Calculate the value.
PV = 140,000 / (1.14)¹³
PV = 140,000 / 5.40937
PV = 25,880.88
Step 4: State the final answer.
You would need to deposit $25,880.88 today.
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