Question

In 1626, the Dutch bought Manhattan Island, now part of New York City, for $24 worth of merchandise. Suppose that, instead, $24 had been invested in an account that paid 3.5% interest each year. Find the balance in 2008.

Answer 1

The balance in 2008 is $12,229,955.10

Explanation:

In 1626, the Dutch bought $24 worth of merchandise.

instead, $24 had been invested in an account that paid 3.5% interest each year, find the balance in 2008.

2008 - 1626 = 382 years

We calculate by compound interest formula :

A =
`P(1+(r)/(n))^((nt))`

Where P = Principal amount ( $24)

r = Rate of interest 3.5% ( 0.035 )

t = 382 years

n = number of compounding in a year ( 1 )

Now we put the values in formula

`24(1+(0.035)/(1))^((1)(382))`

= 24 ( 1.035 )
`^(382)`

= 24 (509581.462506)

= $12,229,955.10

The balance in 2008 is $12,229,955.10

Answer 2

2008 - 1626 -= 382

24 x (1.305)^382

= 12,229,955,10

Hope this helps