Problema Solution
Two people, Ella and Jane, decide to start saving for retirement. Ella decides to invest $4000 a year into an annuity at the age of 25. At the age of 35 she stops making investments and just leaves the money there. Jane on the other hand, decides to start investing $4000 a year at the age of 40 and invests that money for every year thereafter. Assuming both retire at 70, and that the interest rate both get on their investments is 10% (compounded annually) who has the most money in their account at age 70? Explain why you pick the answer you pick
Answer provided by our tutors
First we will calculate how much money Ella will have after the first 10 years:
R = $4000 is periodic payment
i = 0.1 or 10% the interest per year
n = 35 - 25 = 10 years
S = the future value
S = R((1 + i)^n - 1)/i)
S = 4000((1 + 0.1)^10 - 1)/0.1)
S = $63,749.7
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in the next 70 - 35 = 35 years the amount $63,749.7 is compounded annually with rate of 10%
the future value A = 63,749.7(1 + 0.1)^35
A = $1,791,521.92
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When Ella retires at 70 years of age she will have $1,791,521.92.
Now we will calculate how much money Jane will save
R = $4000
n = 70 - 40 = 30 years
i = 0.1 or 10%
S = R((1 + i)^n - 1)/i)
S = 4000((1 + 0.1)^30 - 1)/0.1
S = $657,976.1
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When Jane retires at 70 years of age she will have $657,976.1.
We conclude that Ella will have more money on her account then Jane when they retire.