for 8 - 9. jeri invests $2000 into an account that earns 5% interest compounded yearly. 8 numeric 1 point…

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. Given $P=$2000$, $r = 0.05$ (since $5%=0.05$), and $t = 4$.

Step2: Substitute values into formula

$A=2000\times(1 + 0.05)^4$. First, calculate $(1 + 0.05)^4=(1.05)^4=1.05\times1.05\times1.05\times1.05 = 1.21550625$. Then, $A = 2000\times1.21550625=2431.0125\approx2431$.

Step3: For question 9, set up the equation

We use the same formula $A = P(1 + r)^t$. Substitute $A = 2685$, $P = 2000$, and $r=0.05$ into the formula: $2685=2000\times(1.05)^t$.

Step4: Solve for $t$

First, divide both sides of the equation by 2000: $\frac{2685}{2000}=(1.05)^t$. So, $1.3425=(1.05)^t$. Take the natural logarithm of both sides: $\ln(1.3425)=t\ln(1.05)$. Then, $t=\frac{\ln(1.3425)}{\ln(1.05)}$. We know that $\ln(1.3425)\approx0.295$ and $\ln(1.05)\approx0.0488$. So, $t=\frac{0.295}{0.0488}\approx6$.

Answer:

8. 2431
9. 6