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Bradley invested an average of $550 per month since age 49 in various securities for his retirement savings. His investments averaged a 7% annual rate of return until he retired at age 73. Given the same monthly investment and rate of return, how much more would Bradley have in his retirement savings had he started investing at age 40? Assume monthly compounding.

User Zerobu
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2 Answers

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Final answer:

Bradley would have approximately $269,027.97 more in his retirement savings if he had started investing at age 40.

Step-by-step explanation:

To calculate how much more Bradley would have in his retirement savings if he had started investing at age 40, we need to compare the total amount he would have saved at age 73 with and without starting at age 40.

By using the formula for compound interest, the total amount Bradley would have saved by age 73 if he started at age 49 can be calculated as follows:

Annual interest rate = 7%

Years of investment = 73 - 49 = 24 years

Monthly investment = $550

Total amount saved = Monthly investment * Number of months *[(1 + (Annual interest rate/12))^(Number of months) - 1] / (Annual interest rate/12)

By substituting the given values into the formula, the total amount saved by age 73 if Bradley started at age 49 is approximately $550 * 24 * [(1 + (0.07/12))^(24) - 1] / (0.07/12) = $374,803.98

To calculate how much more Bradley would have in his retirement savings if he had started at age 40, we can use the same formula with the number of years of investment being 73 - 40 = 33 years.

By substituting the new number of years of investment into the formula, the total amount saved by age 73 if Bradley started at age 40 is approximately $550 * 33 * [(1 + (0.07/12))^(33) - 1] / (0.07/12) = $643,831.95

To find the difference in retirement savings, we subtract the total amount saved starting at age 49 from the total amount saved starting at age 40: $643,831.95 - $374,803.98 = $269,027.97

Therefore, Bradley would have approximately $269,027.97 more in his retirement savings if he had started investing at age 40.

User Radioreve
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2 votes
To estimate the amount Bradley would have at age 73 if he started investing in 40 we use the future annuity formula given by:
A=P[((1+r)^n-1)/r]
where:
P=principle
r=rate
n=time
thus plugging in the values we get:
A=12×550=$6600
n=73-40=33
r=7%
hence
A=6600[((1.07)^33-1)/0.07]
simplifying the ^ we get:
A=784,960.6054
Hence the answer is: $784, 960.6054
User Tsury
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