Question

Tim has an investment account which compounds interest continuously at a rate of 1.6%. He puts $2400 in the account initially. After 5 years, how much does he have in the account?

Round your answer to the nearest whole number.

Answer 1

Using the continuous compound interest formula, A = Pe^(rt), Tim's investment of $2400 at a rate of 1.6% for 5 years will amount to approximately $2567, when rounded to the nearest whole number.

Step-by-step explanation:

To calculate how much Tim will have in his investment account after 5 years with continuous compounding interest, we use the formula for continuous compound interest, which is A = Pert, where P is the principal amount ($2400), r is the annual interest rate (0.016), t is the time in years (5), and e is the base of natural logarithms (approximately 2.71828).

Plugging in the values, Tim's investment after 5 years would be A = 2400e(0.016×5). When we calculate this, we find that A is approximately $2567.30. Therefore, Tim will have around $2567 in the account after 5 years, which is the amount rounded to the nearest whole number.