If you, a 22 year-old engineer, and your employer combine to contribute $2,200 (A 1 ) to your 401(k) retirement account which is projected to earn 7% per year. You expect this amount to increase 3% per year indefinitely. You plan to retire in 40 years (at age 62). What is the compound future amount (F) you should expect? [Hint: There will be 40 EOY payments]
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Solution
This is the case of future value of growing annuity. The future value can be calculated with the use of following formula:
Future Value of Growing Annuity = Annual Payment*[((1+r)^n - (1+g)^n)/(r - g)] where r = rate of return, g = growth rate and n = years.
Since, we are required to calculate the value at the time of retirement and we have been specifically provided in the question that there will be 40 EOY payments, we will take n = 40
___________
Solution:
Here, Annual Payment = $2,200, r = 7%, g = 3% and n = 40
Using these values in the above formula, we get,
Future Value (F) = 2,200*[((1+7%)^40 - (1+3%)^40)/(7% - 3%)] = $644,183.10 (answer)
.
If you- a 22 year-old engineer- and your employer combine to contribut.docx
1. If you, a 22 year-old engineer, and your employer combine to contribute $2,200 (A 1 ) to your
401(k) retirement account which is projected to earn 7% per year. You expect this amount to
increase 3% per year indefinitely. You plan to retire in 40 years (at age 62). What is the
compound future amount (F) you should expect? [Hint: There will be 40 EOY payments]
Show work
Solution
This is the case of future value of growing annuity. The future value can be calculated with the
use of following formula:
Future Value of Growing Annuity = Annual Payment*[((1+r)^n - (1+g)^n)/(r - g)] where r = rate
of return, g = growth rate and n = years.
Since, we are required to calculate the value at the time of retirement and we have been
specifically provided in the question that there will be 40 EOY payments, we will take n = 40
___________
Solution:
Here, Annual Payment = $2,200, r = 7%, g = 3% and n = 40
Using these values in the above formula, we get,
Future Value (F) = 2,200*[((1+7%)^40 - (1+3%)^40)/(7% - 3%)] = $644,183.10 (answer)
![If you, a 22 year-old engineer, and your employer combine to contribute $2,200 (A 1 ) to your
401(k) retirement account which is projected to earn 7% per year. You expect this amount to
increase 3% per year indefinitely. You plan to retire in 40 years (at age 62). What is the
compound future amount (F) you should expect? [Hint: There will be 40 EOY payments]
Show work
Solution
This is the case of future value of growing annuity. The future value can be calculated with the
use of following formula:
Future Value of Growing Annuity = Annual Payment*[((1+r)^n - (1+g)^n)/(r - g)] where r = rate
of return, g = growth rate and n = years.
Since, we are required to calculate the value at the time of retirement and we have been
specifically provided in the question that there will be 40 EOY payments, we will take n = 40
___________
Solution:
Here, Annual Payment = $2,200, r = 7%, g = 3% and n = 40
Using these values in the above formula, we get,
Future Value (F) = 2,200*[((1+7%)^40 - (1+3%)^40)/(7% - 3%)] = $644,183.10 (answer)](https://image.slidesharecdn.com/ifyou-a22year-oldengineer-andyouremployercombinetocontribut-230204001505-cdea80f9/85/If-you-a-22-year-old-engineer-and-your-employer-combine-to-contribut-docx-1-320.jpg)
