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Answer :
Final answer:
To retire with at least $1 million, you would need to invest around $381 per month. If you start investing at age 25, you could retire in your mid 60's.
Explanation:
To calculate how long it would take to retire with at least $1 million, we can use the future value formula for compound interest:
FV = P (1 + r/n)^(nt)
Where:
FV = future value (in this case, $1 million)
P = monthly investment
r = annual interest rate (10% in this case)
n = number of times interest is compounded per year (assuming it is compounded monthly, n = 12)
t = number of years
We are trying to solve for t, so we can rearrange the formula:
t = log(FV/P) / log(1 + r/n)
Substituting in the given values:
t = log(1000000/P) / log(1 + 0.10/12)
The formula to calculate the retirement age when starting at a certain age is:
Retirement age = starting age + t
So, if you start investing at age 25, the retirement age would be:
Retirement age = 25 + t
Based on the calculations, you would need to invest around $381 per month to retire with at least $1 million. And if you started investing at age 25, you could retire in your mid 60's.
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Final answer:
To retire with $1 million at a 10% anticipated rate of return, you would need to invest around $381 per month. Starting at age 25, you could retire in your mid-60s if you consistently invested this amount per month.
Explanation:
To retire with at least $1 million with an anticipated rate of return of 10%, you would need to calculate the monthly investment required to achieve this goal. Using the future value of an ordinary annuity formula, you can determine that investing approximately $381 per month would be necessary. As for the age at which you could retire, it would depend on when you start investing. If you started at age 25, and assuming a consistent monthly investment of $381, you could retire in your mid-60s.
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