Question

Suppose that you are given a choice of receiving your scholarship in the amounts of $5,000 today and $5,000 next year, or receiving $9,000 all at once today. If the interest rate is 10%, which choice should you choose in order to maximize the present value of your scholarship?

Answer 1

Option 1 is more preferable.

Explanation:

As provided, the two options are:

Option 1

$5,000 today and $5,000 next year

The prevailing interest rate is 10%

Therefore, present value of this option

=
`(1)/((1 + 0.1)^0) * 5,000 + (1)/((1 + 0.1)^1) * 5,000`

=
`5,000 * 1 + 5,000 * 0.909 = 9,545`

Option 2

Receiving $9,000 today straight once for all the dues.

Its present value shall be

`(1)/((1 + 0.1)^0) * 9,000`

= 9,000

Since the net present value is more of option 1, the Option 1 shall maximize the value by $545 extra = $9,545 - $9,000