Question

According to legend, in 1626 Manhattan Island was purchased for trinkets worth about $24. If the $24 had been invested at a rate of 6% interest per year, what would be its value in 2006? Compare this with a total of $802.4 billion in assessed values for Manhattan in 2006.

Answer 1

Its value in 2006 would be $99, 183, 639, 920

Explanation:

Use the compounding interest formula for this one, which looks like this in its standard form:

`A(t)=P(1+r)^t`

Our P is the initial amount of $24, the r in decimal form is .06, and the time between 2006 and 1626 in years is 380. Fitting this into our formula we get:

`A(t)=24(1+.06)^(380)` or

`A(t)=24(1.06)^(380)`

First raise the 1.06 to the power of 380 on your calculator and then multiply in 24.

As for the second part of the question, I'm not quite sure how it's supposed to be answered. But maybe you can figure that out according to what the unit normally asks you to do.