complete the table to determine the balance after 1 year in mama bigbucks. account using different methods…

Explanation:

Step1: Recall compound - interest formulas

The general 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), $n$ is the number of times compounded per year, and $t$ is the number of years. For continuous compounding, the formula is $A = Pe^{rt}$. Given $P = 20000$ and $r=0.03$ and $t = 1$.

Step2: Calculate for yearly compounding

When compounded yearly, $n = 1$. The equation is $A=20000(1 + 0.03)^1=20000\times1.03$. $A=20000\times1.03 = 20600$.

Step3: Calculate for semi - annual compounding

When compounded semi - annually, $n = 2$. The equation is $A=20000(1+\frac{0.03}{2})^{2\times1}=20000(1 + 0.015)^2$. $A=20000\times(1.015)^2=20000\times1.030225 = 20604.5$.

Step4: Calculate for quarterly compounding

When compounded quarterly, $n = 4$. The equation is $A=20000(1+\frac{0.03}{4})^{4\times1}=20000(1 + 0.0075)^4$. $(1 + 0.0075)^4=1.0075^4\approx1.030339$. So $A=20000\times1.030339 = 20606.78$.

Step5: Calculate for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$. Substitute $P = 20000$, $r = 0.03$ and $t = 1$. $A=20000e^{0.03\times1}=20000e^{0.03}\approx20000\times1.030455 = 20609.1$.

Method of Compounding	Equation	Balance
Yearly	$20000(1.03)^1$	$20600$
Semi - Annually	$20000(1+\frac{0.03}{2})^2$	$20604.5$
Quarterly	$20000(1+\frac{0.03}{4})^4$	$20606.78$
Continuously	$20000e^{0.03}$	$20609.1$

Answer:

Method of Compounding	Equation	Balance
Yearly	$20000(1.03)^1$	$20600$
Semi - Annually	$20000(1+\frac{0.03}{2})^2$	$20604.5$
Quarterly	$20000(1+\frac{0.03}{4})^4$	$20606.78$
Continuously	$20000e^{0.03}$	$20609.1$