Assume “today” is July 17, 2020. II. (30 points) 200 years ago today, on July 17, 1820, Jeb Springfield established a Rainy Day Fund (RDF) for his town, with these rules: Rule 1. Money withdrawn from the RDF can be spent for anything the town wants. Rule 2. A withdrawal of money from the RDF is permitted only once every 100 years. Here is the RDF’s history to date: July 17, 1820 July 17, 1821 July 17, 1920 July 17, 1920 July 17, 2020 Jeb Springfield contributes $2 to establish the RDF. Inspired by Jeb’s gift, the town citizens (as a group) make the first of 100 annual $1 contributions. The citizens make their final $1 contribution; no more money is ever contributed to the RDF. The town withdraws 90% of the RDF’s money and uses it to create Springfield College. The town is considering a withdrawal from the RDF. Assume the RDF earns a return of 12% (EAY) on its money. Please answer the following questions: (A) On July 17, 1920, before the withdrawal (and after the final $1 contribution), how much money was in the RDF? (B) Springfield College used half of the RDF withdrawal on July 17, 1920 for construction, and it used the other half to buy a growing annuity with 200 annual payments, with the first one on July 17, 1920 and growing at a rate 8% (EAY) thereafter. How much was the College’s first annuity payment? (C) How much is the College’s annuity payment today, July 17, 2020? (D) How much money is in the RDF today, July 17, 2020? (E) Suppose the town withdraws 90% of this money that is left and divides it into equal portions for each of the town’s 80,000 residents. How much does each resident receive?
PLEASE ANSWER PARTS D AND E
Assume “today” is July 17, 2020.
II. (30 points)
200 years ago today, on July 17, 1820, Jeb Springfield established a Rainy Day Fund (RDF) for his town, with these rules:
Rule 1. Money withdrawn from the RDF can be spent for anything the town wants. Rule 2. A withdrawal of money from the RDF is permitted only once every 100 years.
Here is the RDF’s history to date:
July 17, 1820 July 17, 1821
July 17, 1920 July 17, 1920 July 17, 2020
Jeb Springfield contributes $2 to establish the RDF.
Inspired by Jeb’s gift, the town citizens (as a group) make the first of 100 annual $1 contributions.
The citizens make their final $1 contribution; no more money is ever contributed to the RDF.
The town withdraws 90% of the RDF’s money and uses it to create Springfield College.
The town is considering a withdrawal from the RDF.
Assume the RDF earns a return of 12% (EAY) on its money.
Please answer the following questions:
(A) On July 17, 1920, before the withdrawal (and after the final $1 contribution), how much money was in the RDF?
(B) Springfield College used half of the RDF withdrawal on July 17, 1920 for construction, and it used the other half to buy a growing
(C) How much is the College’s annuity payment today, July 17, 2020?
(D) How much money is in the RDF today, July 17, 2020?
(E) Suppose the town withdraws 90% of this money that is left and divides it into equal portions for each of the town’s 80,000 residents. How much does each resident receive?
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