Question

fatoumata is going to invest in an account paying an interest rate of 1.7% compounded continuously. how much would fatoumata need to invest, to the nearest hundred dollars, for the value of the account to reach $6,300 in 5 years?

Explanation:

Step1: Recall continuous compounding formula

The formula is $A = Pe^{rt}$, where $A$ is final amount, $P$ is principal, $r$ is rate, $t$ is time.

Step2: Identify given values

$A = 6300$, $r = 0.017$, $t = 5$. Rearrange for $P$: $P = \frac{A}{e^{rt}}$.

Step3: Calculate exponent

$rt = 0.017 \times 5 = 0.085$.

Step4: Compute $e^{0.085}$

$e^{0.085} \approx 1.0887$.

Step5: Find $P$

$P = \frac{6300}{1.0887} \approx 5786.5$. Round to nearest hundred: 5800.

Answer:

5800