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Gabrielle just won $2.5 million in the state lottery. She is given the option of receiving a total of $1.3 million now, or she can elect to be paid $100, 000 at the end of each of the next25 years. If Gabrielle can earn 5% annually on her investments, from a strict economic point of view which option should she take?

Sagot :

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Answer:

He should take annuity ahead of lump sum

Explanation:

Given that :

One time lump sum payment = 1,300,000

r = 5%

Period, t = 25 years

Cash flow, C= 100000v

A = C[1 - (1 + r)^-t] ÷ r

Hence,

100000×(1−(1.05)^−25)÷0.05

100000 * (1 - 0.2953027) ÷ 0.05

70469.722 / 0.05

= 1409394.4

The present value of the annuity is

$1,409,394.4

Annuity payment is greater Than lump sum

Gabriella will earn better if she chooses the option of annuity as it will give her better returns on her investment in comparison to a lump sum.

What is annuity?

An annuity is a series of payments made at regular intervals. Examples of annuities are common deposits in a savings account, monthly mortgage payments, monthly insurance payments, and pension payments.

Formula:

[tex]\rm\,PV = P\times\,\dfrac{1 - (1+r)^{-n}}{r}\\[/tex]

We can calculate the present value of annuity by the information given:

[tex]\rm\,Lump\,sump\,amount = \$1,300,000\\Value\,of\,payment = \$100,000\\\\r= 5\%\\\\Period\,n= 25\,years\\\\\rm\,PV = 100,000\times\,\dfrac{1 - (1+0.05)^{-25}}{0.05}\\\\\rm\,PV = 100,000\times\,\dfrac{(1 - 0.2953027 )}{0.05}\\\\\rm\,PV = \dfrac{70,469.722}{0.05}\\\\= \$\,1,409,394.4[/tex]

The value of present value of the annuity is equal to $1,409,394.4

Hence, the present value of the annuity is greater than lumpsum amount. Gabriella should choose the option of annuity over lumpsum amount.

To learn more about annuity, refer to the link:

https://brainly.com/question/25792915

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