$20,000 loan compounded 2 times a year

$A = 20000(1 + \frac{0.04}{2})^{2 \cdot 2}$

$A = 20000(1 + 0.02)^{4}$

$A = 20000(1.02)^{4}$

$A \approx 20000\left( 1.082 \right)$

$A = 21640.00$

$A - P:$ $21,640 - $20,000 = $1,640 interest.

$20,000 compounded 4 times a year

$A = 20000(1 + \frac{0.04}{4})^{4 \cdot 2}$

$A = 20000(1 + 0.01)^{8}$

$A = 20000(1.01)^{8}$

$A \approx 20000\left( 1.083 \right)$

$A = 21660.00$

$A - P:$ $21,660 - $20,000 = $1,660 interest.

8 years compounded bimonthly

$P = 500,\ r = 0.12,\ n = 6$, and $t = 8$

$A = 500(1 + \frac{0.12}{6})^{6 \cdot 8}$

$A = 500(1 + 0.02)^{48}$

$A = 500(1.02)^{48}$

$A \approx 500\left( 2.587 \right)$

$A = 1293.50$

$A-P:$ $(\$ 1,293.50 - \$ 500) = \$ 793.50$

Rita will earn $793.50 on this investment after eight years.

6 years compounded monthly

$P = 1500,\ r = 0.08,\ n = 12$, and $t = 6$

$A = 1500(1 + \frac{0.08}{12})^{12 \cdot 6}$

$A \approx 1500(1 + 0.007)^{72}$

$A = 1500(1.007)^{72}$

$A \approx 1500\left( 1.652 \right)$

$A = 2478.00$

$A-P:$ $(\$ 2,478 - \$ 1,500) = \$ 978.00$

Rita will earn $978.00 on this investment after six years.

Loan 1 Compound Interest

$P = 100000,\ r = 0.02,\ n = 1$, and $t = 30$

$A = 100000(1 + \frac{0.02}{1})^{1 \cdot 30}$

$A = 100000(1 + 0.02)^{30}$

$A = 100000(1.02)^{30}$

$A \approx 100000\left( 1.811 \right)$

$A = 181100$

$A-P:$ $(\$ 181,100 - \$ 100,000)$ $= \$ 81,100$

Loan 2 Simple Interest

$P = 100000,\ r = 0.02,$ and $t = 30$

$I = Prt$

$I = 100000 \cdot 0.02 \cdot 30$

$I = 60000$