Question

lamonte is going to invest in an account paying an interest rate of 4% compounded continuously. how much would lamonte need to invest, to the nearest cent, for the value of the account to reach $12,300 in 8 years?

Explanation:

Step1: Recall continuous compound formula

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

• $A$ = final amount, $P$ = principal (initial investment), $r$ = annual interest rate, $t$ = time in years, $e$ = Euler's number (~2.71828)

Step2: Rearrange to solve for $P$

Isolate $P$ by dividing both sides by $e^{rt}$:
$P = \frac{A}{e^{rt}}$

Step3: Substitute given values

$A = 12300$, $r = 0.04$, $t = 8$
$P = \frac{12300}{e^{0.04 \times 8}}$

Step4: Calculate exponent and denominator

First compute the exponent: $0.04 \times 8 = 0.32$
Then $e^{0.32} \approx 1.377127764$

Step5: Compute final principal value

$P = \frac{12300}{1.377127764} \approx 8931.53$

Answer:

$\$8931.53$