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On May 24, 1626, Peter Minuit and other colonists acquired Manhattan with Native Americans, with groceries that worth around 1,050$ in nowadays USD, it was said that if Native Americans exchanged the goods into money, stored them into a bank with compound interest, they would have got so much money that they can buy back the entire Manhattan, assuming:

1.The Manhattan worths exactly 1.4$ Trillion dollars.

2.The bank can hold unlimited money.

3.The money is in the bank for a total of 390 years.

4.The money is in nowadays USD (a.k.a. After accounting for inflation.=1,050 USD)

4.The yearly interest rate is 5% & The bank uses compound interest.

5.The colonists are still alive.

 

Answer the following questions:

1.Are they able to buy Manhattan back after 390 years? (2016)

2.(Following 1.)

If yes: Calculate the year when they reached their goal.

If no: Calculate the year when they finally got enough money.

3.What is the minimum interest rate for them to reach equal to or over 1.4$ Trillion dollars in 390 years?

(Round up to the nearest hundredths.)

Jeffes02  Aug 21, 2017
edited by Jeffes02  Aug 21, 2017
edited by Jeffes02  Aug 21, 2017
edited by Jeffes02  Aug 21, 2017
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2+0 Answers

 #1
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Answer the following questions:

1.Are they able to buy Manhattan back after 390 years? (2016)

2.(Following 1.)

If yes: Calculate the year when they reached their goal.

If no: Calculate the year when they finally got enough money.

2.What is the minimum interest rate for them to reach equal to or over 1.4$ Trillion dollars in 390 years?

(Round up to the nearest hundredths.)

 

This is the simple TVM formula that you would use to get your answers:

FV = PV x [1 + R]^N, where FV=Future value, PV=Present value, R= Interest rate per period, N=Number of periods. 

1. FV =1,050 x [1.05]^390

    FV =$192,759,564,461.49 - No, they could not Manhattan back.

2. $1.4E12 =$1,050 x 1.05^N - take the log of both sides and solve for N, and you should get N=~431 years, or the year 2057 AD, when they would have $1.4 x 10^12.

3. 1.4E12 = $1,050 x [1+R]^390 - Again, you would use logs to find the Interest Rate, which comes to =5.54% compounded annually for 390 years.

Guest Aug 21, 2017
 #2
avatar+178 
-1

It looks like that you have been studying economics to know that formula XD, didn't waste my time waiting two hours for an detailed answer, thank you for clarifying my question random stranger :D

(Time to hack into Federal reserves and change the interest rate now)

Jeffes02  Aug 21, 2017

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