2200 dollars is placed in an account with an annual interest rate of 6.5%. to the nearest year, how long…

Explanation:

Step1: Use compound - interest formula

The compound - interest formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Here, we can also use the simple - interest formula $A=P(1 + rt)$ for simplicity since we are not given the compounding frequency and assume simple interest. $P = 2200$, $r=0.065$, and $A = 14100$. Substitute these values into the formula: $14100=2200(1 + 0.065t)$.

Step2: Simplify the equation

First, divide both sides of the equation by 2200: $\frac{14100}{2200}=1 + 0.065t$. So, $\frac{141}{22}=1 + 0.065t$. Then, $\frac{141}{22}-1=0.065t$. Calculate $\frac{141}{22}-1=\frac{141 - 22}{22}=\frac{119}{22}$. So, $\frac{119}{22}=0.065t$.

Step3: Solve for $t$

$t=\frac{119}{22\times0.065}$. $22\times0.065 = 1.43$. Then $t=\frac{119}{1.43}\approx83.22$.

Answer:

83 years