Question

1. jackie invests $7000 at a rate of 3.5% compounded continuously. how much will her investment be worth in 5 years?

Explanation:

Step1: Recall continuous compound formula

The formula for continuous compounding is $A = Pe^{rt}$, where:

• $P$ = principal amount,
• $r$ = annual interest rate (decimal),
• $t$ = time in years,
• $A$ = final amount.

Step2: Convert rate to decimal

$r = \frac{3.5}{100} = 0.035$

Step3: Substitute values into formula

$P = 7000$, $r=0.035$, $t=5$
$A = 7000e^{(0.035 \times 5)}$

Step4: Calculate exponent term

$0.035 \times 5 = 0.175$
$A = 7000e^{0.175}$

Step5: Compute final amount

$e^{0.175} \approx 1.1912$
$A \approx 7000 \times 1.1912 = 8338.40$

Answer:

$\$8338.40$ (rounded to the nearest cent)