you deposit $1900 in an account earning 5% interest compounded quarterly. how much will you have in the…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.

Step2: Convert values to appropriate form

Given $P=$1900$, $r = 5%=0.05$, $n = 4$ (compounded quarterly), and $t = 6$ years.

Step3: Substitute values into the formula

$A=1900(1 +\frac{0.05}{4})^{4\times6}$. First, calculate the value inside the parentheses: $\frac{0.05}{4}=0.0125$, then $1+\frac{0.05}{4}=1 + 0.0125=1.0125$. Next, calculate the exponent: $4\times6 = 24$. So, $A = 1900\times(1.0125)^{24}$.

Step4: Calculate $(1.0125)^{24}$

Using a calculator, $(1.0125)^{24}\approx1.348850152$.

Step5: Calculate $A$

$A=1900\times1.348850152\approx2562.82$.

Answer:

$2562.82$