Final answer:
After 13 years in an account with a 5.7% annual interest rate compounded continuously, you would have approximately $1678.92, option C, using the continuous compounding formula A = Pe^(rt) with principal $800, rate 0.057, and time 13 years.
Step-by-step explanation:
To calculate the amount of money you will have after 13 years in an account that pays 5.7% annual interest compounded continuously, you can use the formula for continuous compounding, which is A = Pe^(rt). Here, 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 (in decimal), and t is the time the money is invested for in years.
The principal amount (P) is $800, the interest rate (r) is 5.7% or 0.057 in decimal form, and the time (t) is 13 years. Plugging these values into the formula, we get:
A = $800 e^(0.057 × 13)
Now we calculate the exponent:
A = $800 e^(0.741)
Next, we calculate e raised to the power of 0.741, which is approximately 2.098:
A = $800 × 2.098
And finally we find A:
A = $1678.92
Therefore, after 13 years, you will have approximately $1678.92, which corresponds to option C.