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