Question

if $535 is invested at an interest rate of 7% per year and is compounded continuously, how much will the investment be worth in 15 years? use the continuous compound interest formula: $a = pe^{rt}$. options: $1,625.93; $1,528.84; $666.65; $573.79

Explanation:

Step1: Identify given values

$P = 535$, $r = 0.07$, $t = 15$

Step2: Substitute into formula

$$A = 535 \times e^{0.07 \times 15}$$

Step3: Calculate exponent term

$0.07 \times 15 = 1.05$, so $A = 535 \times e^{1.05}$

Step4: Compute final amount

$e^{1.05} \approx 2.8576$, so $A \approx 535 \times 2.8576 = 1528.816$

Answer:

$1,528.84$