2200 dollars is placed in an account with an annual interest rate of 7.25%. how much will be in the account…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the interest rate to decimal

Given $r = 7.25%=0.0725$, $P = 2200$, and $t = 29$.

Step3: Substitute values into the formula

$A=2200\times(1 + 0.0725)^{29}$. First, calculate $(1 + 0.0725)^{29}$. Let $x=(1 + 0.0725)^{29}$. Using the formula $a^n=e^{n\ln(a)}$, we have $\ln(x)=29\ln(1.0725)$. $\ln(1.0725)\approx0.0699$ and $29\ln(1.0725)\approx29\times0.0699 = 2.0271$. Then $x = e^{2.0271}\approx7.607$. So $A = 2200\times7.607=16735.4$.

Answer:

$$16735.40$