Asked by maths
You plan to retire in 30 years and would like to have $1,000,000 in investments. How much money would you have to invest today at a 9% annual interest rate compounded daily to reach your goal in 30 years? (Assume all years have 365 days. Round your answer to the nearest cent.)
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Answers
Answered by
GPT 3.5
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($1,000,000)
P = the principal investment amount (what we are trying to solve for)
r = the annual interest rate (0.09)
n = the number of times the interest is compounded per year (365)
t = the number of years the money is invested for (30)
Plugging in the values and solving for P:
$1,000,000 = P(1 + 0.09/365)^(365*30)
$1,000,000 = P(1 + 0.0002465753)^10950
$1,000,000 = P(1.090)?
$1,000,000 = 9.82871P
P = $101,725.41
Therefore, you would need to invest approximately $101,725.41 today at a 9% annual interest rate compounded daily to reach $1,000,000 in investments in 30 years.
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($1,000,000)
P = the principal investment amount (what we are trying to solve for)
r = the annual interest rate (0.09)
n = the number of times the interest is compounded per year (365)
t = the number of years the money is invested for (30)
Plugging in the values and solving for P:
$1,000,000 = P(1 + 0.09/365)^(365*30)
$1,000,000 = P(1 + 0.0002465753)^10950
$1,000,000 = P(1.090)?
$1,000,000 = 9.82871P
P = $101,725.41
Therefore, you would need to invest approximately $101,725.41 today at a 9% annual interest rate compounded daily to reach $1,000,000 in investments in 30 years.
Answered by
GPT 3.5
I apologize for the mistake in the calculation. Let's correct it:
A = P(1 + r/n)^(nt)
$1,000,000 = P(1 + 0.09/365)^(365*30)
$1,000,000 = P(1 + 0.0002465753)^(10,950)
$1,000,000 = P(1.0002465753)^(10,950)
$1,000,000 = P(9.56760702)
P = $1,000,000 / 9.56760702
P = $104,485.65
Therefore, you would need to invest approximately $104,485.65 today at a 9% annual interest rate compounded daily to reach $1,000,000 in investments in 30 years. Thank you for your patience.
A = P(1 + r/n)^(nt)
$1,000,000 = P(1 + 0.09/365)^(365*30)
$1,000,000 = P(1 + 0.0002465753)^(10,950)
$1,000,000 = P(1.0002465753)^(10,950)
$1,000,000 = P(9.56760702)
P = $1,000,000 / 9.56760702
P = $104,485.65
Therefore, you would need to invest approximately $104,485.65 today at a 9% annual interest rate compounded daily to reach $1,000,000 in investments in 30 years. Thank you for your patience.
Answered by
GPT 3.5
I apologize for the previous errors. Let's correct the calculation:
A = P(1 + r/n)^(nt)
$1,000,000 = P(1 + 0.09/365)^(365*30)
$1,000,000 = P(1 + 0.0002465753424657534)^(10,950)
$1,000,000 = P(1.0002465753424657534)^(10,950)
$1,000,000 = P(9.386313632164491)
P = $1,000,000 / 9.386313632164491
P = $106,522.94
Therefore, you would need to invest approximately $67,227.88 today at a 9% annual interest rate compounded daily to reach $1,000,000 in investments in 30 years. Thank you for your patience.
A = P(1 + r/n)^(nt)
$1,000,000 = P(1 + 0.09/365)^(365*30)
$1,000,000 = P(1 + 0.0002465753424657534)^(10,950)
$1,000,000 = P(1.0002465753424657534)^(10,950)
$1,000,000 = P(9.386313632164491)
P = $1,000,000 / 9.386313632164491
P = $106,522.94
Therefore, you would need to invest approximately $67,227.88 today at a 9% annual interest rate compounded daily to reach $1,000,000 in investments in 30 years. Thank you for your patience.
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