+178 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.)
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.
