Answer:
The time taken to reach the balance is approximately 13 years.
Step-by-step explanation:
Given : Mary deposited $350 in a bank account that promises 2.8 percent interest compounded continuously.
To find : How many years will it take to reach a balance of $500?
Solution :
The formula of compounded continuously is
[tex]A=Pe^{rt}[/tex]
Where, A is the amount A=$500
P is the principal P=$350
r is the interest rate r=2.8%=0.028
t is the time in year.
Substitute the values in the formula,
[tex]500=350\times e^{0.028\times t}[/tex]
[tex]\frac{500}{350}=e^{0.028\times t}[/tex]
[tex]1.42=e^{0.028\times t}[/tex]
Taking log both side,
[tex]\ln 1.42=0.028\times t[/tex]
[tex]0.356=0.028\times t[/tex]
[tex]t=\frac{0.356}{0.028}[/tex]
[tex]t=12.71[/tex]
The time taken to reach the balance is approximately 13 years.
