13) first national bank is offering 4.25% interest on an account. susan makes an initial deposit of $20,000…

Explanation:

Step1: Identify values for simple - interest

Principal $P = 20000$, rate $r=0.0425$ (since $4.25%=0.0425$), time $t = 20$. Using the simple - interest formula $I=Prt$. $I=20000\times0.0425\times20$

Step2: Calculate simple - interest

$I = 20000\times0.0425\times20=17000$

Step3: Identify values for compound - interest (annually)

$P = 20000$, $r = 0.0425$, $n = 1$ (compounded annually), $t=20$. The compound - interest formula is $A=P(1 +\frac{r}{n})^{nt}$, and $I=A - P$. $A=20000(1+\frac{0.0425}{1})^{1\times20}=20000(1.0425)^{20}$ $A\approx20000\times2.20804\approx44160.8$ $I=A - P=44160.8 - 20000=24160.8$

Step4: Identify values for compound - interest (quarterly)

$P = 20000$, $r = 0.0425$, $n = 4$ (compounded quarterly), $t = 20$. $A=20000(1+\frac{0.0425}{4})^{4\times20}=20000(1 + 0.010625)^{80}$ $A\approx20000\times2.22107\approx44421.4$ $I=A - P=44421.4-20000 = 24421.4$

Step5: Identify values for compound - interest (monthly)

$P = 20000$, $r = 0.0425$, $n = 12$ (compounded monthly), $t = 20$. $A=20000(1+\frac{0.0425}{12})^{12\times20}=20000(1+\frac{0.0425}{12})^{240}$ $A\approx20000\times2.22497\approx44499.4$ $I=A - P=44499.4 - 20000=24499.4$

Answer:

a) The simple interest is $17000$. b) The compound interest compounded annually is approximately $24160.8$. c) The compound interest compounded quarterly is approximately $24421.4$. d) The compound interest compounded monthly is approximately $24499.4$.