SOLUTION: When interest is compounded quarterly (4 times a year) at an annual rate of 6%, the rate of interest for each quarter is {{{ 0.06/4 }}} , and the number of times that interest is a

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: When interest is compounded quarterly (4 times a year) at an annual rate of 6%, the rate of interest for each quarter is {{{ 0.06/4 }}} , and the number of times that interest is a      Log On


   



Question 946945: When interest is compounded quarterly (4 times a year) at an annual rate of 6%, the rate of interest for each quarter is +0.06%2F4+ , and the number of times that interest is added in t years is
4t. After how many years will an investment of $100 compounded quarterly at 6% annually be worth at least $450? (Use the formula +A+%28n%29+=+A+%280%29+%28+1+%2B+r%2Fn+%29+%5Ent+ ).

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
+4t+ times in +t+ years
---------------------------
(b)
+A+%28n%29+=+A+%280%29+%28+1+%2B+r%2Fn+%29+%5Ent+
+r+=+.06+
+n+=+4+
+A%280%29+=+100+
+A%284%29+=+450+
----------------
+450+=+100%2A%28+1+%2B+.06%2F4+%29%5E%28+4%2At+%29+
+450+=+100%2A%28+1.015+%29%5E%28+4t+%29+
+4.5+=+%28+1.015+%29%5E%28+4t+%29+
+log%28+4.5+%29+=+4t%2Alog%28+1.015+%29+
+4t+=+log%28+4.5+%29+%2F+log%28+1.015+%29+
+4t+=+.6532+%2F+.00647+
+4t+=+100.9583+
+t+=+25.2396+
25.2396 years
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check:
+450+=+100%2A%28+1+%2B+.06%2F4+%29%5E%28+4%2A25.2396+%29+
+450+=+1.015%5E100.9584+
+4.5+=+4.49574+
error due to rounding off, I think