If $570 is invested at an interest rate of 4% per year and is compounded continuously, how much will the investment be worth in 10 years? use the continuous compound interest formula: a = pert.

Continuous compounding refers to the potentially infinite number of times compound interest can be calculated and reinvested into an account's balance.
Formula, [tex]\mathrm{A}=\mathrm{Pe}^{\mathrm{rt}}[/tex].
Where A is the principal amount after t number of years, r is the rate at which the principal is been compounded and P is the principal amount.

To find the worth of the investment after a period of 10 years:

Given the principal amount of $570 is invested for a period of 10 years, and at a rate of 4% per year, therefore, the worth of the investment after 10 years will be:

[tex]\mathrm{A}=\$ 570 \times \mathrm{e}^{(0.04 \times 10)}=\$ 850.34[/tex]

Therefore, the worth of the investment after a period of 10 years will be (D) $850.34.

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The correct question is given below:

If $570 is invested at an interest rate of 4% per year and is compounded continuously, how much will the investment be worth in 10 years? Use the continuous compound interest formula: A = Pert.

(A) $593.26

(B) $655.66

(C) $726.74

(D) $850.34