Question

can someone please help with this? i want to make sure i'm doing it right

Liam is saving for a car. He has $4,500 saved up so far but would like to make his money work for him by investing it in a bank. His bank says they will give him 5% on this investment, compounded continuously. If he lets the money sit in the bank for 10 years, how much will he have in his account? Round your answer to the nearest cent (hundredth).

Answer 1

Answer: $7,419.25

Step-by-step explanation:

     We are given an initial amount of $4,500, a continuous interest rate of 5%, and a time of 10 years. Since this is continuous compounding interest, we can use the given formula to solve for how much money he'll have in his account.

     We will use the interest in decimal form, 5% / 100 = 0.05.

Given:

➜ P(t) is value at time t, $P_o$ is the initial amount, r is the rate, and t is the time.

$\dispalystyle P(t) = P_oe^{rt}$

Substitute known values:

$\dispalystyle P(t) =4500*e^{(0.05)(10)}$

Multiply:

$\dispalystyle P(t) =4500*e^{(0.5)}$

Evaluate:

P(t) ≈ $7,419.25

Learn more about calculating continuous compounding interest here: https://brainly.com/question/30761863