SOLUTION:  If 4 years of college are expected to cost $150,000 18 years from now, how much must be deposited now into an account that will average 8% annually in order to save the $150,000?

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Question 761805:  If 4 years of college are expected to cost $150,000 18 years from now, how much must be deposited now into an account that will average 8% annually in order to save the $150,000? By how much would your answer change if you expected 11% annually? 
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +P+ = amount deposited now
Let +A+ = the current savings
After 1st year,
+A+=+P+%2B+.08P+
---------------
After 2nd year,
+A+=+%28+P+%2B+.08P+%29+%2B+.08%2A%28+P+%2B+.08P+%29+
+A+=+%28+P+%2B+.08P+%29%2A%28+1+%2B+.08+%29+
+A+=+P%2A%28+1+%2B+.08+%29%2A%28+1+%2B+.08+%29+
----------------
After 3rd year,

+A+=+P%2A%28+1+%2B+.08+%29%2A%28+1+%2B+.08+%29%2A%28+1+%2B+.08+%29+
+A+=+P%2A%28+1+%2B+.08+%29%5E3+
----------------------
So, this is the general rule:
+A+=+P%2A%28+1+%2B+.08+%29%5Et+
where t+ = the number of years since initial deposit
given:
+A+=+150000+
+t+=+18+
+150000+=+P%2A%28+1+%2B+.08+%29%5E18+
+150000+=+P%2A1.08%5E18+
+150000+=+3.996P+
+P+=+37537.35+
$37,537.35 needs to be deposited now
---------------------------------
Rate = 11%
+150000+=+P%2A1.11%5E18+
+150000+=+6.544P+
+P+=+22923.33+
$22,923.33 needs to be deposited now