Question

Suppose you deposit $600 into an account that pays 5% annual interest, compounded continuously. How much will you have in the account in four years? Use the formula A(t) = Pe^(rt).

A) $671.46
B) $713.88
C) $746.22
D) $782.92

Answer 1

To calculate the amount of money you will have in the account after 4 years with continuous compounding, use the formula A(t) = Pe^(rt) and plug in the given values. The answer is approximately $713.88.

Step-by-step explanation:

To calculate the amount of money you will have in the account after 4 years with continuous compounding, we can use the formula A(t) = Pe^(rt), where A(t) is the amount after time t, P is the initial deposit, e is the base of the natural logarithm, r is the interest rate, and t is the time in years.

In this case, P = $600, r = 0.05, and t = 4. Plugging in these values into the formula, we have A(4) = $600 * e^(0.05 * 4).

Calculating this using a calculator, we find that A(4) is approximately $713.88.

Therefore, the answer is option B) $713.88.