Final answer:
The question involves calculating the future value of an investment using the compound interest formula. Substituting the given values into the formula does not yield an answer that matches any of the provided options, which may indicate a calculation error.
Step-by-step explanation:
The question asks to calculate the future value of a $3400 investment at 3.75% interest compounded annually after 14 years. To find the future value of an investment with compound interest, we use the formula A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Substituting the given values into the formula, we get:
A = 3400(1 + 0.0375/1)^(1\*14)
A = 3400(1 + 0.0375)^14
A = 3400(1.0375)^14
A = 3400\*1.7397
A = $5912.58 (rounded to two decimal places)
However, this value does not match any of the options provided, suggesting a potential miscalculation or typo. Reevaluating the calculation is recommended to ensure accuracy.