4. tim has $5800 in his savings account that has 3.25% apr. how long will it take to become $7000?

Explanation:

Step1: Use compound - interest formula (assuming annual compounding, $A = P(1 + r)^t$)

Let $P = 5800$, $A=7000$, and $r = 0.0325$. Then the equation is $7000 = 5800(1 + 0.0325)^t$.

Step2: Simplify the equation

First, divide both sides of the equation by 5800: $\frac{7000}{5800}=(1.0325)^t$, so $1.2069=(1.0325)^t$.

Step3: Take the natural logarithm of both sides

$\ln(1.2069)=\ln(1.0325^t)$. Using the property of logarithms $\ln(a^b)=b\ln(a)$, we get $\ln(1.2069)=t\ln(1.0325)$.

Step4: Solve for $t$

$t=\frac{\ln(1.2069)}{\ln(1.0325)}$. Calculate $\ln(1.2069)\approx0.188$ and $\ln(1.0325)\approx0.032$. Then $t=\frac{0.188}{0.032}\approx 5.875$.

Answer:

Approximately 5.88 years.