Questions: Time Value Money VE=VB(1+r)^n Where VE : ending value VB : beginning value r : interest rate usually quoted as annual percentage rate (APR) n : number of compounding periods You invest 2000 into a savings account that earns 2% APR. How much is your 2000 worth after 15 years? Include units and round your answer to the nearest dollar (the nearest unit). Answer: O

Time Value Money VE=VB(1+r)^n Where VE : ending value VB : beginning value r : interest rate usually quoted as annual percentage rate (APR) n : number of compounding periods You invest 2000 into a savings account that earns 2% APR. How much is your 2000 worth after 15 years? Include units and round your answer to the nearest dollar (the nearest unit). Answer: O
Transcript text: Time Value Money \[ V_{E}=V_{B}(1+r)^{n} \] Where $V_{E}$ : ending value $\mathrm{V}_{\mathrm{B}}$ : beginning value $r$ : interest rate usually quoted as annual percentage rate (APR) n : number of compounding periods You invest \$2000 into a savings account that earns 2\% APR. How much is your \$2000 worth after 15 years? Include units and round your answer to the nearest dollar (the nearest unit). Answer: O\$ $\square$
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Solution

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Solution Steps

To solve this problem, we will use the formula for compound interest to calculate the ending value of an investment. We have the beginning value (\$2000), the annual interest rate (2% or 0.02 as a decimal), and the number of compounding periods (15 years). We will plug these values into the formula to find the ending value.

Step 1: Identify the Variables

We are given the following values:

  • \( V_B = 2000 \) (beginning value in dollars)
  • \( r = 0.02 \) (annual interest rate as a decimal)
  • \( n = 15 \) (number of compounding periods in years)
Step 2: Apply the Compound Interest Formula

We will use the formula for compound interest: \[ V_E = V_B(1 + r)^n \] Substituting the known values into the formula: \[ V_E = 2000(1 + 0.02)^{15} \]

Step 3: Calculate the Ending Value

Calculating the expression: \[ V_E = 2000(1.02)^{15} \approx 2000 \times 1.349353 \approx 2691.7366766482596 \] Rounding this value to the nearest dollar gives: \[ V_E \approx 2692 \]

Final Answer

The value of the investment after 15 years is \(\boxed{2692}\).

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