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John has received a college scholarship and can choose whether to receive it as an immediate one-time payment of $10000 or as a series of four equal payments (at the end of each year), each totaling $3000. Assume that John has a discount rate of 10%. Only considering TVM principles, which option is most valuable to John?

A. There is not enough information to determine the answer.
B. Series of four payments of $3000 each.
C. Immediate payment of $10000.
D. Both scenarios are equal.

Respuesta :

Answer:

Option "C" is the correct answer to the following statement.

Explanation:

Given:

Monthly Payment = $3,000

Number of payment = 4

Discount Rate = 10% = 0.10

Present value = ?

Calculation:

[tex]Present value = PMT[\frac{1-(1+r)^{-n}}{r} ]Present value = PMT[\frac{1-(1.1)^{-4}}{0.1} ]\\Present value = PMT[\frac{1-(1+0.1)^{-4}}{0.1} ]\\Present value = PMT[\frac{1-(1.1)^{-4}}{0.1} ]\\\\Present value = PMT[\frac{1-0.683013455}{0.1} ]\\Present value = 3000[\frac{0.31698654}{0.1}]\\\\Present value = 3000[3.16986545 ]\\Present value = 9509.59[/tex]

Therefore , he immediate payment of $10000.

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