Final answer:
Peter will have approximately $10,723.82 in the savings account after five years if he invested $8,000 at 6% interest compounded continuously. The calculation uses the formula for continuous compounding interest, demonstrating the effective growth of an investment over time.
Step-by-step explanation:
The question pertains to the calculation of the future value of an investment with continuous compounding interest. Given that Peter invested $8,000 at a 6% interest rate compounded continuously, we can use the formula for continuous compounding A = Pert to calculate the amount in the savings account after five years. Here, P is the principal amount of $8,000, r is the annual interest rate of 0.06, t is the time in years, which is 5, and e is the base of the natural logarithm, approximately equal to 2.71828.
Plugging the values into the formula gives us A = 8000 × e(0.06 × 5). Calculating this yields A to be approximately $10,723.82, which means the correct answer is (b) $10,723.82. This calculation makes it evident that continuous compounding interest can lead to a significant increase in the investment amount over a period of time.