Final answer:
To calculate Shane's account balance after 5 years with a 4% semiannual interest rate, the compound interest formula is used, giving a result of $4,266.465, which does not match any of the given answer choices.
Step-by-step explanation:
The question asks us to calculate the future value of an investment with compound interest. Shane invested $3,500 in an account that pays 4% interest semiannually. To find out how much money he will have in his account in 5 years, we can use the compound interest formula: A = P(1 + r/n)^(nt), where:
- P is the principal amount ($3,500)
- r is the annual interest rate (0.04 for 4%)
- n is the number of times interest is compounded per year (2 for semiannual)
- t is the time in years (5)
The calculation would be as follows:
A = $3,500(1 + 0.04/2)^(2*5)
A = $3,500(1 + 0.02)^(10)
A = $3,500(1.02)^10
A = $3,500(1.21899)
A = $4,266.465
However, this amount does not match any of the answer choices provided, suggesting there may be a miscalculation or the options given are incorrect. Please double-check the interest rate, compounding frequency, timeframe, or the choices provided.