Question

$25,000 are deposited into an account with a 3.45% interest rate, compounded semi - annually (2 times per year). find the accumulated amount after 25 years. hint: $a = p(1+\frac{r}{k})^{kt}$

Explanation:

Step1: Identify given values

$P = 25000$, $r = 0.0345$, $k = 2$, $t = 25$

Step2: Calculate periodic rate

$\frac{r}{k} = \frac{0.0345}{2} = 0.01725$

Step3: Calculate total compound periods

$kt = 2 \times 25 = 50$

Step4: Compute accumulated amount

$A = 25000(1 + 0.01725)^{50}$
First calculate $(1.01725)^{50} \approx 2.3773$
Then $A = 25000 \times 2.3773$

Answer:

$\approx 59432.50$