Answer:
Instructions are listed below
Explanation:
Giving the following information:
At the end of each year, she invests the accumulated savings ($1,825) in a brokerage account with an expected annual return of 8%. She will invest for 45 years.
A) We need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= annual deposit
FV= {1825[(1.08^45)-1]}/0.08= $705,372.75
B) n= 25
FV= {1825[(1.08^25)-1]}/0.08= $133,418.34
C) FV= 705,372.75 A=?
We need to isolate A:
A= (FV*i)/{[(1+i)^n]-1}
A=(705,372.75*0.08)/[(1.08^25)-1]
A= $9,648.64
The amount that a student accumulate at the age of 65 years of old is $7,05,372.75, and if the 40 years old investor began in this manner then it would be at the age of 65 years is 1,33,418.34,
and the amount of annual payment would be 9,648.
Investment is the faithfulness of an asset to achieve an addition in value over a period of time and the Investment requires a sacrifice of some present asset, such as time, money, or effort.
Computations:
The accumulated amount at the age 65 is :
according to the question, annuity = $1,825,
n(Time) = 45 years,
r(Rate) = 8%
We need to find the future value of $1,825 at the age of 65.
[tex]\text{Future Value} = \dfrac{A(1+i)^n-1}{i}\\\\\\\text{Future Value} =\dfrac{\$1,825(1+8\%)^4^5-1}{8\%}\\\\\\\text{Future Value} =\$7,05,372.75.[/tex]
Then, at the age of 65 when 40 years old investor invested is:
n= 25 years.
[tex]\text{Future Value} = \dfrac{A(1+i)^n-1}{i}\\\\\\\text{Future Value} =\dfrac{\$1,825(1+8\%)^2^5-1}{8\%}\\\\\\\text{Future Value} =\$1,33,418.34[/tex]
Then, we need to reserve A :
[tex]A= \dfrac{\text{(Future Value}) i}{(1+i)^n-1}\\\\A= \dfrac{\text{(\$7,05,372.75}) (8\%)}{(1+8\%)^2^5-1}\\\\A=\$9,648.64.[/tex]
Therefore, the annual deposit would be $9,648.64.
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