Solve the problem.
-A deposit of $11,000 is made in an account that earns 8% interest compounded quarterly. The balance in the account after n quarters is given by the sequence $$\mathrm { a } _ { \mathrm { n } } = 11,000 \left( 1 + \frac { 0.08 } { 4 } \right) ^ { \mathrm { n } } , \mathrm { n } = 1,2,3 , \ldots$$
Find the balance in the account after 4 years.
A) $\$ 15,100.64$
B) $\$ 5491.14$
C) $\$ 11,906.75$
D) $\$ 4257.14$

Question

Quizplus · Accepted Answer

After 4 years, there are 16 quarters since interest is compounded quarterly. Thus, we want to find $a_{16}$:

\begin{align*}
a_{16} &= 11,000\left(1+\frac{0.08}{4}ight)^{16}\
&=11,000\left(1.02ight)^{16}\
&\approx \boxed{\$15,100.64}
\end{align*}

Solve the Problem an=11,000(1+0.084)n,n=1,2,3,…\mathrm { a } _ { \mathrm { n } } = 11,000 \left( 1 + \frac { 0.08 } { 4 } \right) ^ { \mathrm { n } } , \mathrm { n } = 1,2,3 , \ldotsan​=11,000(1+40.08​)n,n=1,2,3,…

Solve the Problem $\mathrm { a } _ { \mathrm { n } } = 11,000 \left( 1 + \frac { 0.08 } { 4 } \right) ^ { \mathrm { n } } , \mathrm { n } = 1,2,3 , \ldots$