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:
- Calculate \( 1 + 0.08 = 1.08 \)
- Raise \( 1.08 \) to the power of \( 3 \):
\[ 1.08^3 \approx 1.259712 \]
- 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.
3 answers