Tom invests $15,000 in stocks, and the value increases by 8% annually. After three years, what will be approximately the value of his investment?

A. $15,000
B. $20,000
C. $25,000
D. $30,000

1 answer

To calculate the value of Tom's investment after three years with an annual increase of 8%, we can use the formula for compound interest:

\[ A = P(1 + r)^n \]

where:

  • \( A \) is the amount of money accumulated after n years, including interest.
  • \( P \) is the principal amount (the initial amount of money, which is $15,000).
  • \( r \) is the annual interest rate (in decimal form, which is 0.08 for 8%).
  • \( n \) is the number of years the money is invested or borrowed (which is 3 years).

Substituting the values into the formula, we have:

\[ A = 15000(1 + 0.08)^3 \]

Calculating that step-by-step:

  1. Calculate \( 1 + 0.08 = 1.08 \)
  2. Raise \( 1.08 \) to the power of \( 3 \):

\[ 1.08^3 \approx 1.259712 \]

  1. Multiply this result by the principal:

\[ A \approx 15000 \times 1.259712 \approx 18895.68 \]

Thus, after three years, the value of Tom's investment will be approximately $18,896.

Now, looking at the answer choices: A. $15,000 B. $20,000 C. $25,000 D. $30,000

The closest answer to $18,896 is B. $20,000.

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