To solve this problem, we will use the formula for continuous compound interest, which is A = P * e^(rt).

Here,
P = principal amount (the initial amount of money) = $500
r = annual interest rate (in decimal form) = 4% = 0.04
t = time the money is invested for (in years) = 7 years

Substituting these values into the formula, we get:

A = 500 * e^(0.04*7)

Now, calculate the exponent first:

0.04 * 7 = 0.28

So, the equation becomes:

A = 500 * e^0.28

Now, use the value of e (approximately 2.71828) and raise it to the power of 0.28:

e^0.28 ≈ 1.32313

Multiply this result by the initial investment:

A = 500 * 1.32313 ≈ $661.56

So, the amount of money that $500 would grow to after 7 years of being invested at a 4% interest rate, compounded continuously, is approximately $661.56.

Therefore, the closest answer is C. $661.55.

Question

To solve this problem, we will use the formula for continuous compound interest, which is A = P * e^(rt).

Here, 
P = principal amount (the initial amount of money) = $500
r = annual interest rate (in decimal form) = 4% = 0.04
t = time the money is invested for (in years) = 7 years

Substituting these values into the formula, we get:

A = 500 * e^(0.04*7)

Now, calculate the exponent first:

0.04 * 7 = 0.28

So, the equation becomes:

A = 500 * e^0.28

Now, use the value of e (approximately 2.71828) and raise it to the power of 0.28:

e^0.28 ≈ 1.32313

Multiply this result by the initial investment:

A = 500 * 1.32313 ≈ $661.56

So, the amount of money that $500 would grow to after 7 years of being invested at a 4% interest rate, compounded continuously, is approximately $661.56.

Therefore, the closest answer is C. $661.55.

Knowee AI · Accepted Answer