1 calculate the ending balance, to the nearest penny, for the account with 3,000 at 4% for 7 years…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula 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. For continuous compounding, the formula is $A = Pe^{rt}$.

Step2: Solve for semiannual compounding

Given $P = 3000$, $r=0.04$, $n = 2$ (semi - annual), and $t = 7$. $A = 3000(1+\frac{0.04}{2})^{2\times7}=3000(1 + 0.02)^{14}=3000\times1.02^{14}\approx3000\times1.321290966\approx3963.87$

Step3: Solve for monthly compounding

Given $P = 3000$, $r = 0.04$, $n=12$ (monthly), and $t = 7$. $A=3000(1 +\frac{0.04}{12})^{12\times7}=3000(1+\frac{0.04}{12})^{84}\approx3000\times1.322077\approx3966.23$

Step4: Solve for daily compounding

Given $P = 3000$, $r = 0.04$, $n = 365$ (assuming non - leap year), and $t = 7$. $A=3000(1+\frac{0.04}{365})^{365\times7}=3000(1+\frac{0.04}{365})^{2555}\approx3000\times1.322197\approx3966.59$

Step5: Solve for continuous compounding

Given $P = 3000$, $r = 0.04$, and $t = 7$. $A = 3000e^{0.04\times7}=3000e^{0.28}\approx3000\times1.323129\approx3969.39$

Answer:

1. $$3963.87$
2. $$3966.23$
3. $$3966.59$
4. $$3969.39$