SOLUTION: Find the rate at which ​$12,696 compounded annually grows to ​13,824 in 2 years.using a=P(1+r)^t

Algebra ->  Square-cubic-other-roots -> SOLUTION: Find the rate at which ​$12,696 compounded annually grows to ​13,824 in 2 years.using a=P(1+r)^t      Log On


   

Question 1103565: Find the rate at which ​$12,696 compounded annually grows to ​13,824 in 2 years.using a=P(1+r)^t
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39631) About Me  (Show Source):
You can put this solution on YOUR website!
Substitute the given values any time you are ready.

Choose your base for the logarithm, but

log%28%28a%29%29=log%28%28P%29%29%2Blog%28%28%281%2Br%29%5Et%29%29
log%28%28a%29%29-log%28%28P%29%29=t%2Alog%28%281%2Br%29%29

log%28%281%2Br%29%29=%28log%28%28a%29%29-log%28%28P%29%29%29%2Ft
Not yet reached a formula for r, but you can find that easily from what value you find from 1%2Br.

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log%28%281%2Br%29%29=%28log%28%2813824%29%29-log%28%2812696%29%29%29%2F2
log%28%281%2Br%29%29=%284.140634-4.1037%29%2F2
log%28%281%2Br%29%29=0.01847
10%5E0.01847=r%2B1
r%2B1=1.0434
highlight%28r=0.0434%29
rate is 4.3%

Answer by ikleyn(52925) About Me  (Show Source):
You can put this solution on YOUR website!
.
12699*(1+r)^2 = 13824  ====>


(1+r)^2 = 13824%2F12699  ====>


1 + r = sqrt%2813824%2F12699%29  ====>


r = sqrt%2813824%2F12699%29-1 = 0.0433.


Answer.  The rate is 0.0433,  or  4.33%  compounded annually.

Ignore the @josgarithmetic writing.


His approach to solving this problem is  W R O N G.