Final answer:
Connor's account will grow to approximately $78,600 after 12 years due to compound interest at a rate of 2.6% compounded continuously, rounding to the nearest hundred dollars.
This correct answer is d)
Step-by-step explanation:
Connor invested $59,000 in an account that offers 2.6% interest compounded continuously; to calculate the amount in the account after 12 years, we use the formula for continuous compounding:
A = Pert, 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), t is the time in years, and e is the base of the natural logarithm, approximately equal to 2.71828.
We know that P = $59,000, r = 0.026 (2.6% expressed as a decimal), and t = 12 years.
To find A, we compute A = $59,000 × e(0.026 × 12). Upon calculating, we find that A is approximately $78,600 when rounded to the nearest hundred dollars. Therefore, the answer is d) $78,600.
The power of compound interest is evident in this situation as the investment grows over time without any further deposits needed.
As seen in the information provided, compound interest can have a significant impact, especially with larger sums and over long periods. In contrast, had the interest been simple instead of compounded continuously, the total amount would have been less.
This correct answer is d)