SOLUTION: Find the final amount in the following retirement account, in which the rate of return on the account and the regular contribution change over time. $470 per month invested at

Question 1080041: Find the final amount in the following retirement account, in which the rate of return on the account and the regular contribution change over time.
$470 per month invested at 5%, compounded monthly, for 7 years; then $709 per month invested at 7%, compounded monthly, for 7 years.
What is the amount in the account after 14 years?
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I have tried calculating a monthly amount per each year and adding it all together. And I have also tried calculating the monthly amount per year and calculating the interest on top of it. I've also tried using investment calculators and compound interest calculators with no avilal. Either way, my answer is always wrong.
Please let me know the best way to solve this problem with the most simplest steps possible in order to obtain the amount that would be in the account after 14 years.
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
See if this helps:
first 7 years:
i = .05/12 = .004166...
n = 7(12) = 84
amount after 7 years = 470(1.041666...^84 - 1)/.004166..
= 47154.47
This will accumulate for another 7 years at 7% pa, compounded monthly
i = .07/12 = .0058333...
n = 84
amount of first investment
= 47154.47(1.0058333..)^84 = 76861.50
amount of 2nd investment
= 709(1.0058333..^84 - 1)/.005833...
= 76571.28
total = 76861.50+76571.28 = $153,432.78 ☺☺☺☺
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