Annaliese has a mutual fund that compounds annually at 3.5% per annum. Her principal was $750 and her current balance is $954.21. How many years has she had this fund?
+118613 Annaliese has a mutual fund that compounds annually at 3.5% per annum. Her principal was $750 and her current balance is $954.21. How many years has she had this fund?
r=0.035, FV=954.21, P=750 n=?
$$\\FV=P(1+r)^n\\\\
954.21=750(1.035)^n\\\\
\frac{954.21}{750}=1.035^n\\\\
log\;\frac{954.21}{750}=log\;1.035^n\\\\
log\;\frac{954.21}{750}=n\;log\;1.035\\\\
n=\frac{log\;\frac{954.21}{750}}{log\;1.035}\\\\$$
n= $${\frac{{log}_{10}\left({\frac{{\mathtt{954.21}}}{{\mathtt{750}}}}\right)}{{log}_{10}\left({\mathtt{1.035}}\right)}} = {\mathtt{7.000\: \!016\: \!844\: \!029\: \!362\: \!8}}$$
7 years.
NOTE: If you have not done logs yet then perhaps you were supposed to just keep multiplying $750 by 1.035 and see how many times you had to do that before you got a total of $954.21
It should be 7 times. :)
+118613 Annaliese has a mutual fund that compounds annually at 3.5% per annum. Her principal was $750 and her current balance is $954.21. How many years has she had this fund?
r=0.035, FV=954.21, P=750 n=?
$$\\FV=P(1+r)^n\\\\
954.21=750(1.035)^n\\\\
\frac{954.21}{750}=1.035^n\\\\
log\;\frac{954.21}{750}=log\;1.035^n\\\\
log\;\frac{954.21}{750}=n\;log\;1.035\\\\
n=\frac{log\;\frac{954.21}{750}}{log\;1.035}\\\\$$
n= $${\frac{{log}_{10}\left({\frac{{\mathtt{954.21}}}{{\mathtt{750}}}}\right)}{{log}_{10}\left({\mathtt{1.035}}\right)}} = {\mathtt{7.000\: \!016\: \!844\: \!029\: \!362\: \!8}}$$
7 years.
NOTE: If you have not done logs yet then perhaps you were supposed to just keep multiplying $750 by 1.035 and see how many times you had to do that before you got a total of $954.21
It should be 7 times. :)
