Respuesta :
Given:
• Amount to save, A = $28,000
,• Time, t = 6 years
,• Interest rate, r = 5.3% ==> 0.053
,• Number of times compounded = quarterly = 4 times
Let's find the amount that must be deposited into the account quarterly.
Apply the formula:
[tex]FV=P(\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}})[/tex]Where:
FV is the future value = $28,000
r = 0.053
n = 4
t = 6 years
Thus, we have:
[tex]28000=P(\frac{(1+\frac{0.053}{4})^{4\times6}-1)}{\frac{0.053}{4}}[/tex]Let's solve for P.
We have:
[tex]\begin{gathered} 28000=P(\frac{(1+0.01325)^{24}-1}{0.01325}) \\ \\ 28000=P(\frac{(1.01325)^{24}-1)^{}}{0.01325}) \\ \\ 28000=P(\frac{1.371509114-1}{0.01325}) \\ \\ 28000=P(\frac{0.371509114}{0.01325}) \end{gathered}[/tex]Solving further:
[tex]28000=P(28.0384237)[/tex]Divide both sides by 28.0384237:
[tex]\begin{gathered} \frac{28000}{28.0384237}=\frac{P(28.0384237)}{28.0384237} \\ \\ 998.6=P \\ \\ P=998.6 \end{gathered}[/tex]Therefore, the amount that must be deposited quarterly into the account is $998.60
ANSWER:
$998.60
