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According to an old myth, native americans sold the island of manhattan about 400 years ago for $24. if they had invested this amount at an interest rate of 7 percent per year, approximately how much would they have had today? $3.6 billion $13.6 trillion $2,030 $10,272

User Ognjenkl
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2 Answers

6 votes

Final answer:

If the Native Americans had invested $24 at a 7 percent annual interest rate, compounded annually, for 400 years, they would have a sum that surpasses trillions of dollars, aligning with the $13.6 trillion figure, though an exact calculation is required to determine the precise amount.

Step-by-step explanation:

If the Native Americans had invested $24 at an interest rate of 7 percent per year, we would need to calculate the future value of this investment over approximately 400 years. To solve this, we can use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($24), r is the annual interest rate (0.07), and n is the number of times that interest is compounded per year. For simplicity, if we compound annually, this gives us t as the number of years (400 in this case).

Applying these values to the formula, we get A = 24(1 + 0.07/1)^(1*400). This results in a huge number, one that would be significantly larger than $3.6 billion, $13.6 trillion, $2,030, or $10,272. In fact, using a calculator, we can see that the investment would grow to a figure that surpasses trillions of dollars, more in line with the $13.6 trillion option, although an exact calculation would be needed to confirm the precise figure.

User SiarheiK
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2 votes

Answer:

The correct choice from given options is "$13.6 trillion".

Step-by-step explanation:

Native Americans sold the island of Manhattan about 400 years ago for $24

n = number of years = 400

Amount spent on island = $24

Interest rate of invested amount = 7 percent per year

r = 7% = 0.07

cost today = ?

By using the formula;

Cost today= (1+r)ⁿ x Amount spent on island

= (1+0.07)⁴⁰⁰ x $24

= $13.6 trillion

User Heather Hins
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