Question

Find the amount of money that will be accumulated in a savings account if $3800 is invested at 4.0% for 24 years and the interest is compounded continuously. Round your answer to two decimal places.

Answer 1

$9,954.32

Explanation:

Where:

A = the future amount (the accumulated amount)

P = the principal amount (initial investment) = $3800

r = annual interest rate (as a decimal) = 4.0% = 0.04

t = the number of years = 24

e = Euler's number, approximately equal to 2.71828

Now, plug in the values and calculate:

A = 3800 * e^(0.04 * 24)

A ≈ 3800 * 2.71828^(0.96)

A ≈ 3800 * 2.616295

A ≈ $9,954.32 (rounded to two decimal places)

So, the amount of money that will be accumulated in the savings account after 24 years with continuous compounding is approximately $9,954.32.