Q1) Crowd funding is a practice whereby which a project is funded by raising small amounts of money from a large number of people. The process (crowd funding) has been primarily be used for charitable causes or for uplifting projects that helps a large group of people. Let us assume that a country named Disney Land with a population of 200 million individuals asks its people to denote to the following Dream projects: S. No. Project Name Total Cost Years to finish Use

1 Grandfather clock Rs. 1000,000 1 For the childrens poem Hickory Dickory Dock 2 Disney-Land Rs. 10,000,000,000 5 Family fun and play. 3 Pay off Debt Rs. 18,000,000,000,000 10 Helping the people and the economy. 1. Consider first the Grandfather clock used in the poem Hickory Dickory Dock. The poem is itself is beloved to children and is time-less in its usefulness. The grandfather clock itself will be placed in time-square allowing all to take their pictures with the clock. Hence, as long as the clock is maintained it will be a popular attraction for families. a) How much money does each individual need to donate to collect the cost for the project? b) Assuming, everyone is able to make one-time donation for the amount (1a) in one month, how much time will it take to collect the money for this project? 2. Consider now Disney-Land. The project is aimed to provide several theme parks based on different cartoon characters loved and enjoyed by children and adults through the last 100 years. Disney-Land is expected to be a very popular attraction for tourists and families and it will help being vital revenue. a) How much money does each individual need to donate to collect the cost for the project? b) Assuming, everyone is able to make one-time donation for the amount (2a) in the second month (as they made the one-time donation to item 1 in their first month), how much time will it take to collect the money for this project? 3. Consider now the most important project of Pay-Off Debt. The project is aimed to rid the country off of external debt. The project will help improve the countrys image, help the economy, improve the value of Disney-bills (currency) and elevate the prestige of dreamers (the population). As such, this is the most important project. a) How much money does each individual need to donate to collect the cost for the project? b) The dreamers (population) are operating under different financial scales. Hence, some

are defined no-dreams (poor), others are classified as essential-dreamers (middle- class) and some are realists (rich). The following table highlights their numbers and the

money they can spare to donate for a charitable cause (per person). Given the table below, how much time will it take (in years) to collect the money for this project. S. No. Population Number Amount of Money, one can donate per month 1 No dreams 110,000,000 0

Copyright 2021 by Dr. Bilal Wajid 2 Essential dreamers 80,000,000 250 3 Realists 10,000,000 50 c) Given the debt needs to be paid in a period of 10 years, how much does each essential dreamer and realist need to donate per month to collect the money in 10 years? d) Regretfully, debts do not work this way. They have an interest which accumulates over time. Let assume that interest is (small) at the rate of 5% per annum. Meaning, if the principal amount of Rs. 100, then after one year, the amount becomes Rs. 105 = Rs. 100 (principal amount) + 5 (interest payment). Make a table of the growing external debt of Disney-Land starting with principal amount of Rs. 18,000,000,000,000/- in year 2021 and an interest of 5% per amount for a period of 10 years beginning 2021 to 2031. Year Principal amount 2021 18,000,000,000,000 2022 2023 2031

e) Given the debt needs to be paid in a period of 10 years, how much does each essential dreamer and realist need now to donate per month to collect the money in 10 years given the table you made in part (3d)? f) Given that Essential dreamers are unable to pay the money calculated in (3e). Assume that the maximum essential dreamers can pay is Rs. 400/month. How much do realists need to pay per month to reach the intended target of making payment in 10 years? We will assume that realists are forced (via super-tax) to pay this amount:

S. No. Population Number Amount of Money, one can donate per month 1 No dreams 110,000,000 0 2 Essential dreamers 80,000,000 400 3 Realists 10,000,000 ? g) Given the new table found in (3f) (keeping the amounts fixed), the CEO and board of Governors of Disney-Land (the producers and directors) decide that they should not wait to collect all the money to pay off the debt, rather they should pay each year whatever is collected so as to reduce the principal amount each year. Therefore, given this new information fill the following table from year 2021 to 2031: Year (A) Principal amount (B) Interest amount (5%)

(C) Donations Collected

(D) Remaining Debt (D) = (A) + (B) (C)

2021 18,000,000,000,000 0 (start) 2022 2023 2031

Copyright 2021 by Dr. Bilal Wajid h) However, debts do not entirely run this way. Each year Disney-Land takes in more and more debt, all the while making interest payments of previous debt. Let us assume that Disney Land takes more debt at the rate of 10% of previous debt, fill the following table from year 2021 to 2031: Year (A) Principal amount (B) Interest amount (5%)

(C) New Debt (10%) (D) Donations Collected

(E) Remaining Debt = (A) + (B) + (C) - (D)

2021 18,000,000,000,000 0 (start) 0 (start) 2022 2023 2031

i) Assuming crowdfunding is the only option, what do Dreamers need to do get out of debt in 10-year time frame? Discrete Structures need it solved theoratically

2 250 Essential dreamers Realists 80,000,000 10,000,000 3 Q1) Crowd funding is a practice whereby which a project is funded by raising small amounts of money from a large number of people. The process (crowd funding) has been primarily be used for charitable causes or for uplifting projects that helps a large group of people. 50 h) However, debts do not entirely run this way. Each year "Disney-Land" takes in more and more debt, all the while making interest payments of previous debt. Let us assume that "Disney Land"takes more debt at the rate of 10% of previous debt, fill the following table from year 2021 to 2031: : Let us assume that a country named "Disney Land" with a population of 200 million individuals asks its people to denote to the following Dream" projects: : s. Project Name Total Cost Years to Use Year (A) Principal amount No. finish c) Given the debt needs to be paid in a period of 10 years, how much does each 'essential dreamer' and 'realist need to donate per month to collect the money in 10 years? d) Regretfully, debts do not work this way. They have an interest which accumulates over time. Let assume that interest is (small) at the rate of 5% per annum. Meaning, if the principal amount of Rs. 100, then after one year, the amount becomes Rs. 105 = Rs. 100 (principal amount) + 5 (interest payment). Make a table of the growing external debt of "Disney-Land" starting with principal amount of Rs. 18,000,000,000,000/- in year 2021 and an interest of 5% per amount for a period of 10 years beginning 2021 to 2031. (6) Interest (C) New Debt (D) Donations (E) Remaining Debt = amount (596) (1096) Collected (A) + (B) + (C) - (D) 0 (start) 0 (start) 2021 18,000,000,000,000 1 1 2022 2 Grandfather clock Disney-Land Pay off Debt Rs. 1000,000 Rs. 10,000,000,000 Rs. 18,000,000,000,000 5 For the children's poem "Hickory Dickory Dock Family fun and play, Helping the people and the economy. 2023 3 10 2031 Year Principal amount 18,000,000,000,000 2021 i) Assuming crowdfunding is the only option, what do Dreamers need to do get out of debt 2022 in 10-year time frame? 2023 1. Consider first the "Grandfather clock used in the poem "Hickory Dickory Dock." The poem is itself is beloved to children and is time-less in its usefulness. The grandfather clock itself will be placed in "time-square" allowing all to take their pictures with the clock. Hence, as long as the clock is maintained it will be a popular attraction for families. a) How much money does each individual need to donate to collect the cost for the project? b) Assuming, everyone is able to make one-time donation for the amount (1a) in one month, how much time will it take to collect the money for this project? 2031 2. Consider now "Disney-Land." The project is aimed to provide several theme parks based on different cartoon characters loved and enjoyed by children and adults through the last 100 years. Disney-Land is expected to be a very popular attraction for tourists and families and it will help being vital revenue. a) How much money does each individual need to donate to collect the cost for the project? b) Assuming, everyone is able to make one-time donation for the amount (2a) in the second month (as they made the one-time donation to item 1 in their first month), how much time will it take to collect the money for this project? e) Given the debt needs to be paid in a period of 10 years, how much does each 'essential dreamer' and 'realist' need now to donate per month to collect the money in 10 years given the table you made in part (3d)? f) Given that 'Essential dreamers' are unable to pay the money calculated in (3e). Assume that the maximum essential dreamers can pay is Rs. 400/month. How much do 'realists' need to pay per month to reach the intended target of making payment in 10 years? We will assume that 'realists' are forced (via super-tax) to pay this amount: S. No. Population Number Amount of Money, one can donate per month 1 0 2 No dreams Essential dreamers Realists 110,000,000 80,000,000 10,000,000 400 3 ? 3. Consider now the most important project of Pay-off Debt." The project is aimed to rid the " country off of external debt. The project will help improve the country's image, help the economy, improve the value of "Disney-bills" (currency) and elevate the prestige of "dreamers" (the population). As such, this is the most important project. a) How much money does each individual need to donate to collect the cost for the project? b) The "dreamers" (population) are operating under different financial scales. Hence, some are defined 'no-dreams' (poor), others are classified as 'essential-dreamers' (middle- class) and some are 'realists' (rich). The following table highlights their numbers and the money they can spare to donate for a charitable cause (per person). Given the table below, how much time will it take in years) to collect the money for this project. g) Given the new table found in (3f) (keeping the amounts fixed), the CEO and board of Governors of Disney-Land (the producers and directors) decide that they should not wait to collect all the money to pay off the debt, rather they should pay each year whatever is collected so as to reduce the principal amount each year. Therefore, given this new information fill the following table from year 2021 to 2031: Year (A) Principal amount (B) Interest (C) Donations (0) Remaining Debt amount (5%) Collected (D) = (A) + (B)-(C) 0 (start) 2021 18,000,000,000,000 S. No. Population Number Amount of Money, one can donate per month 0 2022 1 No dreams 110,000,000 2023 2031 2 250 Essential dreamers Realists 80,000,000 10,000,000 3 Q1) Crowd funding is a practice whereby which a project is funded by raising small amounts of money from a large number of people. The process (crowd funding) has been primarily be used for charitable causes or for uplifting projects that helps a large group of people. 50 h) However, debts do not entirely run this way. Each year "Disney-Land" takes in more and more debt, all the while making interest payments of previous debt. Let us assume that "Disney Land"takes more debt at the rate of 10% of previous debt, fill the following table from year 2021 to 2031: : Let us assume that a country named "Disney Land" with a population of 200 million individuals asks its people to denote to the following Dream" projects: : s. Project Name Total Cost Years to Use Year (A) Principal amount No. finish c) Given the debt needs to be paid in a period of 10 years, how much does each 'essential dreamer' and 'realist need to donate per month to collect the money in 10 years? d) Regretfully, debts do not work this way. They have an interest which accumulates over time. Let assume that interest is (small) at the rate of 5% per annum. Meaning, if the principal amount of Rs. 100, then after one year, the amount becomes Rs. 105 = Rs. 100 (principal amount) + 5 (interest payment). Make a table of the growing external debt of "Disney-Land" starting with principal amount of Rs. 18,000,000,000,000/- in year 2021 and an interest of 5% per amount for a period of 10 years beginning 2021 to 2031. (6) Interest (C) New Debt (D) Donations (E) Remaining Debt = amount (596) (1096) Collected (A) + (B) + (C) - (D) 0 (start) 0 (start) 2021 18,000,000,000,000 1 1 2022 2 Grandfather clock Disney-Land Pay off Debt Rs. 1000,000 Rs. 10,000,000,000 Rs. 18,000,000,000,000 5 For the children's poem "Hickory Dickory Dock Family fun and play, Helping the people and the economy. 2023 3 10 2031 Year Principal amount 18,000,000,000,000 2021 i) Assuming crowdfunding is the only option, what do Dreamers need to do get out of debt 2022 in 10-year time frame? 2023 1. Consider first the "Grandfather clock used in the poem "Hickory Dickory Dock." The poem is itself is beloved to children and is time-less in its usefulness. The grandfather clock itself will be placed in "time-square" allowing all to take their pictures with the clock. Hence, as long as the clock is maintained it will be a popular attraction for families. a) How much money does each individual need to donate to collect the cost for the project? b) Assuming, everyone is able to make one-time donation for the amount (1a) in one month, how much time will it take to collect the money for this project? 2031 2. Consider now "Disney-Land." The project is aimed to provide several theme parks based on different cartoon characters loved and enjoyed by children and adults through the last 100 years. Disney-Land is expected to be a very popular attraction for tourists and families and it will help being vital revenue. a) How much money does each individual need to donate to collect the cost for the project? b) Assuming, everyone is able to make one-time donation for the amount (2a) in the second month (as they made the one-time donation to item 1 in their first month), how much time will it take to collect the money for this project? e) Given the debt needs to be paid in a period of 10 years, how much does each 'essential dreamer' and 'realist' need now to donate per month to collect the money in 10 years given the table you made in part (3d)? f) Given that 'Essential dreamers' are unable to pay the money calculated in (3e). Assume that the maximum essential dreamers can pay is Rs. 400/month. How much do 'realists' need to pay per month to reach the intended target of making payment in 10 years? We will assume that 'realists' are forced (via super-tax) to pay this amount: S. No. Population Number Amount of Money, one can donate per month 1 0 2 No dreams Essential dreamers Realists 110,000,000 80,000,000 10,000,000 400 3 ? 3. Consider now the most important project of Pay-off Debt." The project is aimed to rid the " country off of external debt. The project will help improve the country's image, help the economy, improve the value of "Disney-bills" (currency) and elevate the prestige of "dreamers" (the population). As such, this is the most important project. a) How much money does each individual need to donate to collect the cost for the project? b) The "dreamers" (population) are operating under different financial scales. Hence, some are defined 'no-dreams' (poor), others are classified as 'essential-dreamers' (middle- class) and some are 'realists' (rich). The following table highlights their numbers and the money they can spare to donate for a charitable cause (per person). Given the table below, how much time will it take in years) to collect the money for this project. g) Given the new table found in (3f) (keeping the amounts fixed), the CEO and board of Governors of Disney-Land (the producers and directors) decide that they should not wait to collect all the money to pay off the debt, rather they should pay each year whatever is collected so as to reduce the principal amount each year. Therefore, given this new information fill the following table from year 2021 to 2031: Year (A) Principal amount (B) Interest (C) Donations (0) Remaining Debt amount (5%) Collected (D) = (A) + (B)-(C) 0 (start) 2021 18,000,000,000,000 S. No. Population Number Amount of Money, one can donate per month 0 2022 1 No dreams 110,000,000 2023 2031