multiple choice 1 point\nsteve invests $1,800 in an account that earns 3.7% annual interest, compounded…

multiple choice 1 point\nsteve invests $1,800 in an account that earns 3.7% annual interest, compounded continuously.\nwhat is the approximate value of the account after 10 years?\n$2,466\n$2,589\n$2,601\n$2,606

multiple choice 1 point\nsteve invests $1,800 in an account that earns 3.7% annual interest, compounded continuously.\nwhat is the approximate value of the account after 10 years?\n$2,466\n$2,589\n$2,601\n$2,606

Answer

Explanation:

Step1: Recall the continuous - compounding formula

The formula for continuous compounding is (A = Pe^{rt}), where (P) is the principal amount, (r) is the annual interest rate (in decimal form), (t) is the time in years, and (e\approx2.71828). Given (P = 1800), (r=0.037), and (t = 10).

Step2: Substitute the values into the formula

Substitute (P = 1800), (r = 0.037), and (t=10) into (A=Pe^{rt}). We get (A = 1800\times e^{0.037\times10}=1800\times e^{0.37}).

Step3: Calculate (e^{0.37})

Using a calculator, (e^{0.37}\approx1.4477).

Step4: Calculate the value of (A)

Then (A=1800\times1.4477 = 2605.86\approx2606).

Answer:

($2606)