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5. A company is offering a scholarship to one

employee's child who provides the best essay
describing their future career goals. The
scholarship would consist of $3,000 right away as
well as an annual payment of $5,000 at the end
of each of the next 3 years. If the company
would be willing to give the full scholarship up
front, what would be the equivalent amount
today if the money could earn 8% compounded
annually?

User Lcat
by
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1 Answer

5 votes

if the company were willing to give the full scholarship upfront, the equivalent amount today would be approximately $15,904.39, assuming an 8% annual interest rate compounded annually.

To determine the equivalent amount today, we need to calculate the present value of the future cash flows. We will consider the $3,000 received immediately and the annual payments of $5,000 at the end of each of the next three years.

To calculate the present value, we can use the formula for the present value of a future cash flow:

PV = FV / (1 + r)^n

Where:

PV = Present Value

FV = Future Value

r = Interest rate per compounding period

n = Number of compounding periods

In this case, the interest rate is 8% (0.08) compounded annually. Let's calculate the present value of the annual payments:

PV_annual = $5,000 / (1 + 0.08)^1 + $5,000 / (1 + 0.08)^2 + $5,000 / (1 + 0.08)^3

Simplifying the equation:

PV_annual = $5,000 / 1.08 + $5,000 / 1.08^2 + $5,000 / 1.08^3

PV_annual = $4,629.63 + $4,293.63 + $3,981.13

PV_annual = $12,904.39

Now, let's calculate the present value of the $3,000 received immediately:

PV_immediate = $3,000

To find the equivalent amount today, we sum up the present values of the immediate and annual payments:

Equivalent amount today = PV_immediate + PV_annual

Equivalent amount today = $3,000 + $12,904.39

Equivalent amount today = $15,904.39

User Methnani Bilel
by
8.1k points

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