Question

question 4 12.5 pts jackson deposited $5,000 at 3.8% interest, compounded continuously, when he was 18 years old. how much will be in the account when he is 40 years old if he made no other deposits or withdrawals? $8,800.00 $19,000.19 $11,535.60 $10,691.38

Explanation:

Step1: Determine the time \( t \)

Jackson was 18 and will be 40, so \( t=40 - 18=22 \) years.

Step2: Use the continuous - compounding formula

The formula for continuous compounding is \( A = Pe^{rt} \), where \( P=\$5000 \), \( r = 0.038 \) (since \( 3.8\%=0.038 \)), and \( t = 22 \).
Substitute the values into the formula: \( A=5000\times e^{0.038\times22} \).
First, calculate \( 0.038\times22 = 0.836 \).
Then, find \( e^{0.836}\approx2.307 \).
Finally, \( A = 5000\times2.307=\$11535 \) (approx).

Answer:

\(\$11,535.60\)