xavier invested $66,000 in an account paying an interest rate of 2.5% compounded daily. assuming no deposits…

Answer:

$107945.94$

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula when compounded $n$ 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 compounded per year, $t$ is the number of years, and $A$ is the amount of money in the account after $t$ years.

Step2: Convert values to correct form

Given $P=$66000$, $r = 2.5%=0.025$, $n = 365$ (compounded daily), and $t = 20$ years.

Step3: Substitute values into formula

$A=66000(1 +\frac{0.025}{365})^{365\times20}$. First, calculate the value inside the parentheses: $\frac{0.025}{365}\approx0.0000684932$, and $1+\frac{0.025}{365}=1 + 0.0000684932=1.0000684932$. Then, calculate the exponent: $365\times20 = 7300$. So, $A = 66000\times(1.0000684932)^{7300}$.

Step4: Calculate the final amount

$(1.0000684932)^{7300}\approx1.635544545$. $A=66000\times1.635544545\approx107945.94$.