Question

1A

In 1626, Peter Minuit purchased Manhattan Island from Native Americans for $24 worth of trinkets and beads. Find what the $24 woukd be worth in the year 2020 if it had been deposited in a bank paying 5% interest compounded quarterly. round your answer to the nearest dollar.

1B

The cost of a four year private college education has been estimated to ge $50,000. How large a trust fund paying 5% compounded quarterly, must be established at a childs birth to ensure sufficient funds at age 18? round your answer to the nearest cent.

Answer 1

1.Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value, PV = Present value = $24, r = rate of interest = 5% compounded quarterly. So, quarterly rate = 5% / 4 = 1.25%, n= time period = 2020 -1626 = 394 years or 394 * 4 = 1576 quarters.

now, putting theses values in the above equation, we get,

FV = $24 * (1 + 1.25%)¹⁵⁷⁶

FV = $24 * (1 + 0.0125)¹⁵⁷⁶

FV = $24 * (1.0125)¹⁵⁷⁶

FV = $24 * 318104822.753

FV = $7634515746

So, the amount is worth of $7634515746 in 2020.

2.Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $50000, PV = Present value, r = rate of interest = 5% compounded quarterly. So, quarterly rate = 5% / 4 = 1.25%, n= time period = 18 * 4 = 72 quarters

now, putting theses values in the above equation, we get,

$50000 = PV * (1 + 1.25%)⁷²

$50000 = PV * (1 + 0.0125)⁷²

$50000 = PV * (1.0125)⁷²

$50000 = PV * 2.44592026814

PV = $50000 / 2.44592026814

PV = $20442.20

So, the trust fund should be of $20442.20.