Solution :
a). Interest for the simple interest ![$= 1000 \times 5 \times 2$](https://tex.z-dn.net/?f=%24%3D%201000%20%5Ctimes%205%20%5Ctimes%202%24)
= $ 100
Amount due for the simple interest = $ 1000 + $ 100
= $ 1100
Amount due for the compound interest ![$= 1000 \times (1.05)^2$](https://tex.z-dn.net/?f=%24%3D%201000%20%5Ctimes%20%281.05%29%5E2%24)
= $ 1102.50
Interest for the compound interest = $ 1102.50 - $ 1000
= $ 102.50
b). Interest for the simple interest ![$= 1500 \times 6 \times 5$](https://tex.z-dn.net/?f=%24%3D%201500%20%5Ctimes%206%20%5Ctimes%205%24)
= $ 450
Amount due for the simple interest = $ 1500 + $ 450
= $ 1950
Amount due for the compound interest ![$= 1500 \times (1.06)^5 $](https://tex.z-dn.net/?f=%24%3D%201500%20%5Ctimes%20%281.06%29%5E5%20%24)
= $ 2007.34
Interest for the compound interest = $ 2007.34 - $ 1500
= $ 507.34
c). Interest for the simple interest ![$= 1000 \times 10 \times 10$](https://tex.z-dn.net/?f=%24%3D%201000%20%5Ctimes%2010%20%5Ctimes%2010%24)
= $ 100000
Amount due for the simple interest = $ 10000 + $ 10000
= $ 20000
Amount due for the compound interest ![$= 10000 \times (1.10)^{10}$](https://tex.z-dn.net/?f=%24%3D%2010000%20%5Ctimes%20%281.10%29%5E%7B10%7D%24)
= $ 25937.42
Interest for the compound interest = $ 25937.42 - $ 10000
= $ 15937.42
d). Interest for the simple interest ![$= 25000 \times 15 \times 15$](https://tex.z-dn.net/?f=%24%3D%2025000%20%5Ctimes%2015%20%5Ctimes%2015%24)
= $ 56,2500
Amount due for the simple interest = $ 25000 + $ 56,250
= $ 81,250
Amount due for the compound interest ![$= 25000 \times (1.15)^{15} $](https://tex.z-dn.net/?f=%24%3D%2025000%20%5Ctimes%20%281.15%29%5E%7B15%7D%20%24)
= $ 203,426.54
Interest for the compound interest = $ 203,426.54 - $ 25,000
= $ 178,426.54
e). Interest for the simple interest ![$= 47,750 \times 20 \times 20$](https://tex.z-dn.net/?f=%24%3D%2047%2C750%20%5Ctimes%2020%20%5Ctimes%2020%24)
= $ 191,000
Amount due for the simple interest = $ 47,750 + $ 191,000
= $ 238,750
Amount due for the compound interest ![$= 47,750 \times (1.20)^{20} $](https://tex.z-dn.net/?f=%24%3D%2047%2C750%20%5Ctimes%20%281.20%29%5E%7B20%7D%20%24)
= $ 1,830,620.40
Interest for the compound interest = $ 1,830,620.40 - $ 47,750
= $ 1,782,870.40