micaela invested $1,400 in an account paying an interest rate of 3.6% compounded quarterly. assuming no…

Explanation:

Step1: Identify compound interest formula

The formula for compound interest is: $$A = P\left(1+\frac{r}{n}\right)^{nt}$$ Where:

• $A$ = final amount
• $P$ = principal amount
• $r$ = annual interest rate (decimal)
• $n$ = number of times compounded per year
• $t$ = time in years

Step2: Convert values to correct units

• $P = 1400$
• $r = \frac{3.6}{100} = 0.036$
• $n = 4$ (compounded quarterly)
• $t = 15$

Step3: Substitute values into formula

$$A = 1400\left(1+\frac{0.036}{4}\right)^{4 \times 15}$$

Step4: Simplify the expression

First calculate $\frac{0.036}{4}=0.009$, so $1+0.009=1.009$ Then calculate $4 \times 15=60$ $$A = 1400(1.009)^{60}$$

Step5: Calculate $(1.009)^{60}$

$(1.009)^{60} \approx 1.7137$

Step6: Compute final amount

$$A = 1400 \times 1.7137 \approx 2399.18$$

Answer:

$$2399.18$