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Sagot :
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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