Question

Brooklyn has a goal to save $8,000 to buy a new entertainment system. In order to meet that goal, she deposited $4,132.79 into a savings account. If the account has an interest rate of 4.8% compounded quarterly, approximately when will Brooklyn be able to make the purchase?

Answer 1

\[FC=IC(\frac{i}{100}+1)^{n}\]
Where FC is the goal meet $8000
IC is the inicial capital $4132.79
i the interest every 3 months 4.8% and
n is the number of quarters (groups of 3 months ) that are needed.
So we must take logaritms in both sides of te equation\[\ln FC =\ln( IC+{\frac{i}{100})^{n}\]
Using the rules of logaritms we can obtain
\[n=\frac {\ln FC-\ln IC}{\ln(\frac{i}{100}+1)}\]
So
\[n=\frac {\ln 8000 - \ln 4132.79}{\ln (\frac {4.8}{100}+1)}\]
n=14.04 quartes
n=14.04 /4=3.51 years
n=14.04 x 3= 42.12 months
n=42.12 x 30 = 12136.6 días

Answer 2

The unseen equation is this

So we must take logaritms in both sides of te equation
\[\ln FC =\ \ln {( IC+\ \frac {i} {100} )^{n}}\]