- Look at the following statements related to the derivation of the lump sum formula:

1: Looked at the total for the first couple of compounding periods

2: Found a common process: multiply by (1 + rate)

3: Took a solution that originally had too many terms and reduced it to something manageable

4: Used short-term information (local) to derive a global formula

5: Performed mathematical magic - no way to know how we obtained our formula

In the derivation of the lump sum formula, we

a)all of the above

b)all but 5

c)other

- If a c.d. will
compounded monthly at 3% for 14 years, and William put in $2000,
how much would the c.d. be worth at the end of 14 years?

(a) 2000(1+.03)^{14}

(b) 2000(1+.03/14)^{14*12}

(c) 2000(1+.03/12)^{14*12}

(d) 2000(1+.03/12)^{14}

(e) none of the above

- If a c.d. will
compound annually at 3% for 14 months, and William put in $2000,
how much would the c.d. be worth at the end of 14 months?

(a) 2000(1+.03)^{14}

(b) 2000(1+.03/14)^{14}

(c) 2000(1+.03/12)^{14*12}

(d) 2000(1+.03)^{14/12}

(e) none of the above

- Which of the following are true?

a) The word interest comes from a similar phrase for "that which is between"

b) Charging interest has been around since at least Babylonian times.

c) Interest rates were once 220%

d) Both b) and c)

e) All of a), b) and c)

- In the case of Benjamin Franklin's fund

a) The earned rate of a fund is the same as the lent rate that is charged to borrow the money in the fund.

b) To find the earned rate of a fund, we can calculate a weighted average rate using the rates each part of the fund actually receives (or loses).

c) To find the earned rate of a fund, we can use the beginning and ending values of the fund and calculate the rate in Excel using the lump sum formula.

d) Both a) and c)

e) Both b) and c)

The 5%*lent rate*marks the expected returns if all the money is lent out and paid back. It stayed constant. The*average earned rate*fluctuates and captures the rate the fund actually receives in a given timeframe-- the cities couldn't find enough borrowers and some that borrowed didn't pay what they owed, so the average earned rate was lower.

- Was the lump sum formula approprate to use in the case of the Benjamin
Franklin fund, when money was going in and out of the account?

a) No - Whoops, we should have used a different formula as it is not a lump sum.

b) Yes - there is no principal money added in during each 100 year period - only the lump principal that Benjamin Franklin designated. The money coming in is only as the loan (a part of the lump sum) and it's*interest*. When we derived the lump sum formula in class, we added the annual earned interest to the amount that was in the account at the beginning of the year to solve for the savings at the end of the end of the year. We repeated this process with each successive year and found a general lump sum formula. By looking at the derivation of the formula, it is clear that earned interest is already accounted for within the lump sum formula, so this is the appropriate formula to use in this case.

c) Yes - We had to use 2 lump sum formulas - one for the first hundred years and one for the second hundred years - because Franklin's plan designated that the fund pay out part of it's money to the cities and states at the end of the first hundred years, so a new lump sum principal amount needed to be used at the start of the second hundred years

d) Both b) and c)

e) None of the above

*An investment in knowledge pays the best interest*[Benjamin Franklin]

- If we put in $100 now and leave it there for 25 years compounded monthly
at 5% how much
**interest ($)**will we have earned?

a) $110.95

b) $248.12

c) $348.12

d) $29550.97

e) none of the above