In order to help get you started, this Sample Ben Word document contains the shell of the paper along with the general lump sum formula, the lump sum formula for the Plan for the First Hundred Years, the Excel chart, and a sample section on the Plan for the Second Hundred Years. You will change this sample so that it is in your own words in order to reflect your own writing style. ��� indicates additional writing. Dr. Sarah

Introduction

�

Plan for the First Hundred Years and the Excel Chart

�

The general lump sum formula is a mathematical equation that is used to solve for the total amount of money that will be in an account after depositing a certain amount of money all at once and leaving it to earn interest for a certain number of years. Since Ben Franklin�s codicil designated that the interest would compound annually, in this case, the general lump sum formula states that

savings = principal (1 + rate)^years

where principal is the amount of money that we deposit as a lump sum.

�

131000 = 1000 (1+ rate)¹⁰⁰

�

	A	B	C	D
1	Info	Time	Money	Average Rate
2	Ben's Plan	100 years	131000	0.0499599
3	Ben's Plan	200 years	4061000	0.0499599
4	Boston	100 years	391000	0.045787863
5	Philly	100 years	172350	0.037255968
6	Boston	200 years	5000000	0.039895503
7	Philly	200 years	2256952	0.041343887

Table 1: Excel Chart

�

Plan for the Second Hundred Years

Ben Franklin proposed that the savings be divided up at the end of the first hundred years. His codicil stipulated that each city should use approximately three-quarters of their earnings for projects that would benefit the public. In a plan that was similar to his plan for the first hundred years, the remaining funds, approximately 31,000 pounds, were to be used for the next hundred years in order to loan money to young married apprentices in order to help them start their own businesses. While Ben Franklin calculated that the savings in each city at the end of the second hundred years would total 4,061,000 pounds, his codicil did not include the planned interest rate for the loans. Yet, the codicil did specify the lump sum principal (31,000 pounds), the number of years that the money would earn interest via the loan process (100 years) and the total intended savings (4,061,000), and so we can set up the lump sum formula with these numbers plugged in:

4061000 = 31000 (1+ rate)¹⁰⁰

We used Excel to solve for the unknown rate in the formula. In row 3 of the excel chart in Table 1, we see that a lent rate of 4.99599% in D3 was planned for the growth of 31,000 pounds to the earnings of 4,061,000 pounds in C3. At the end of the second hundred years, Ben Franklin stipulated that these earnings should be divided between the city and state in both Boston and Philadelphia. Each state would receive three-quarters of the money, or approximately 3,000,000 pounds, while each city would receive the remaining one-quarter, approximately 1,061,000 pounds. He thought that the government should then decide what to do with these funds: �not presuming to carry my views farther.�

Actual First Hundred Years in Boston

�

Actual First Hundred Years in Philadelphia

�

Difference Between the Lent Rate and Earned Rate

�

Actual Second Hundred Years in Boston

�

Actual Second Hundred Years in Philadelphia

�

Disposition of the Funds in Boston

�

Disposition of the Funds in Philadelphia

�

Comparison of Boston and Philadelphia's Earnings and Fund

�

Disposition in Relationship to the Goals Listed in the Codicil

�

Conclusion

�