+154 Assume that $5000 can be invested at rate of 5%/a compounded monthly
a.) determine the value of the investment after 6 years
A=Ao(1+i)n
A=5000(1.05)6
=6700$
b.) determione the length of time to the nearest year, required for the investement to tripple in value ?
+129899 Your set-up to "a" is slightly incorrect...it should be
A = 5000(1+.05/12)12*6 = $6745.09
For "b', the amount invested doesn't really matter....let's see why......
3A = A (1 + .05/12)12t divide through by A....
3 = (1 + .05/12)12t (see why "A" doesn't matter??) .......take the log of both sides
log3 = log (1 + .05/12)12t and by a property of logs, we can write
log3 = (12t)*log(1 + .05/12) divide both sides by 12*log(1 + .05/12)
[log3] / (12*log(1 + .05/12)) = t = about 22.018 years
+129899 Your set-up to "a" is slightly incorrect...it should be
A = 5000(1+.05/12)12*6 = $6745.09
For "b', the amount invested doesn't really matter....let's see why......
3A = A (1 + .05/12)12t divide through by A....
3 = (1 + .05/12)12t (see why "A" doesn't matter??) .......take the log of both sides
log3 = log (1 + .05/12)12t and by a property of logs, we can write
log3 = (12t)*log(1 + .05/12) divide both sides by 12*log(1 + .05/12)
[log3] / (12*log(1 + .05/12)) = t = about 22.018 years
