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
\(A=Pe^{rt}\)
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,
\(500=350\times e^{0.028\times t}\)
\(\frac{500}{350}=e^{0.028\times t}\)
\(1.42=e^{0.028\times t}\)
Taking log both side,
\(\ln 1.42=0.028\times t\)
\(0.356=0.028\times t\)
\(t=\frac{0.356}{0.028}\)
\(t=12.71\)
The time taken to reach the balance is approximately 13 years.
