question 3 (2 points) samantha deposits $15000 into the park street bank. the account pays 4.12% annual…

question 3 (2 points) samantha deposits $15000 into the park street bank. the account pays 4.12% annual interest, compounded daily. to the nearest cent, how much is in the account at the end of 3 years? $ blank 1:

question 3 (2 points) samantha deposits $15000 into the park street bank. the account pays 4.12% annual interest, compounded daily. to the nearest cent, how much is in the account at the end of 3 years? $ blank 1:

Answer

Explanation:

Step1: Identify compound - interest formula

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

Step2: Convert values to appropriate form

Given $P=$15000$, $r = 4.12%=0.0412$, $n = 365$ (compounded daily), and $t = 3$ years.

Step3: Substitute values into formula

$A=15000(1 +\frac{0.0412}{365})^{365\times3}$. First, calculate $\frac{0.0412}{365}=0.000112877$. Then $1+\frac{0.0412}{365}=1 + 0.000112877=1.000112877$. Next, $365\times3 = 1095$. So $A = 15000\times(1.000112877)^{1095}$. Using a calculator, $(1.000112877)^{1095}\approx1.130777$. Then $A=15000\times1.130777=$16961.66$.

Answer:

$16961.66$