Question

Improvements at a Harley-Davidson Plant are estimated to be $7.8 million. Construction is expected to take three years. What is the future worth of the project in year 3 at an interest rate of 6% per year compounded quarterly, assuming the funds are allocated (a) completely at time 0, and (b) equally at the end of each year?

Answer 1

A) -9,289,924.80

B) -8,268,360‬.00

Step-by-step explanation:

To solve for the first part, we have to solve for the futue value of a lump sum

`Principal \: (1+ r)^(time) = Amount`

Principal 7,800,000.00

time 3.00

rate 0.06000

`7800000 \: (1+ 0.06)^(3) = Amount`

Amount 9,289,924.80

As this is future worth, te value will be negative.

Then, we solve for thre payment equally at the end of each year:

7,800,000 / 3 = 2,600,000

1st 2nd 3rd

=------/------/------/

The first capitalize for 2 period

the second for one period and te third for none.

`2600000 \: (1+ 0.06)^(2) = Amount`

Amount 2,921,360.00

`2600000 \: (1+ 0.06)^(1) = Amount`

Amount 2,756,000.00

Third year 2,600,000

Total worth = 8,268,360‬