Question 1183345: I am really struggling with this problem, I got help from a math tutor and we could not figure it out, I believe we used the annuity formula. Please can someone help me with it?
Suppose you invest $160 a month for 5 years into an account earning 9% compounded monthly. After 5 years, you leave the money, without making additional deposits, in the account for another 25 years. How much will you have in the end?
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Suppose instead you didn't invest anything for the first 5 years, then deposited $160 a month for 25 years into an account earning 9% compounded monthly. How much will you have in the end?
Answer by Solver92311(821)   (Show Source):
You can put this solution on YOUR website!
The first thing you need to do is calculate the future value of the 5 years of regular payments. This is an annuity calculation.
You don't specify, but I'm going to assume you mean an ordinary annuity where the periodic deposits are made at the end of each period (as opposed to an annuity due where payments are made at the beginning)
^{nt}\,-\,1}{\frac{r}{n}}\])
Where  is the amount of the cash deposit at the end of each period,  is the interest rate expressed as a decimal,  is the number of compounding periods per year, and  is the number of years.
For this problem:  ,  ,  , and  , to wit:
^{(12)(5)}\,-\,1}{\frac{0.09}{12}}\])
Then you need to calculate the Future Value of a one-time investment in the amount just calculated at the same interest and compounding for 25 years:
^{nt})
^{(12)(25)})
You can do your own arithmetic.
For the other part of the question, just use the Ordinary Annuity formula but for 25 years instead of 5.
John
My calculator said it, I believe it, that settles it
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