Question

jason is going to invest $720 and leave it in an account for 6 years. assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for jason to end up with $930?

Explanation:

Step1: Recall continuous compounding formula

The formula is $A = Pe^{rt}$, where $A=930$, $P=720$, $t=6$.

Step2: Isolate exponential term

Divide both sides by $P$: $\frac{A}{P} = e^{rt}$ → $\frac{930}{720} = e^{6r}$

Step3: Simplify left side

$\frac{930}{720} ≈ 1.2917$

Step4: Take natural log of both sides

$\ln(1.2917) = 6r$

Step5: Calculate ln value

$\ln(1.2917) ≈ 0.2554$

Step6: Solve for r

$r = \frac{0.2554}{6} ≈ 0.0426$ → convert to percentage: $4.26\%$

Answer:

4.26%