SOLUTION: Please help me solve this problem: Suppose you want to accumulate $25,000 as down payment on a house and the best you can do is to put aside $200 a month. If you deposit this a

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Question 319235: Please help me solve this problem:
Suppose you want to accumulate $25,000 as down payment on a house and the best you can do is to put aside $200 a month. If you deposit this amount at the beginning of each month in an account that credits 0.75% interest monthly, how long will it take you to attain your goal?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let r+=+.0075 (.75%)
After the 1st month, I have
200+%2B+200r+=+200%2A%281+%2B+r%29
After the 2nd month, I have
200%2A%281+%2B+r%29+%2B+200%2A%281+%2B+r%29%2Ar+=+200%2A%281+%2B+r%29%2A%281+%2B+r%29
After the 3rd month, I have
200%2A%281+%2B+r%29%5E2+%2A%281+%2B+r%29+=+200%2A%281+%2B+r%29%5E3
----------------------------
I can write the formula
200%2A%281.0075%29%5En+=+25000
where n = number of months invested
%281.0075%29%5En+=+125
Solve this using logs
n%2Alog%281.0075%29+=+log%28125%29
n+=+log%28125%29%2Flog%281.0075%29
n+=+2.09691%2F+.003245
n+=+646.2
it will take 646.2 months or 53.8 years