Answer Key 11.6

[latexpage]

1. 1. \(\begin{array}{rrl}
      \\ \\ \\ \\ \\ \\ \\
      A&=&\text{find}\hspace{0.25in} P=\$500\hspace{0.25in} r=0.04\hspace{0.25in} n=1 \hspace{0.25in} t=10 \\ \\
      A&=&500\left(1+\dfrac{0.04}{1}\right)^{10} \\ \\
      A&=&500(1.04)^{10} \\ \\
      A&=&\$740.12
      \end{array}\)
   2. \(\begin{array}{rrl}
      \\ \\ \\ \\ \\ \\ \\
      A&=&\text{find}\hspace{0.25in} P=\$600\hspace{0.25in} r=0.06\hspace{0.25in} n=1 \hspace{0.25in} t=6 \\ \\
      A&=&600\left(1+\dfrac{0.06}{1}\right)^6 \\ \\
      A&=&600(1.06)^6 \\ \\
      A&=&\$851.11
      \end{array}\)
   3. \(\begin{array}{rrl}
      \\ \\ \\ \\ \\ \\ \\
      A&=&\text{find}\hspace{0.25in} P=\$750\hspace{0.25in} r=0.03\hspace{0.25in} n=1 \hspace{0.25in} t=8 \\ \\
      A&=&750\left(1+\dfrac{0.03}{1}\right)^8 \\ \\
      A&=&750(1.03)^8 \\ \\
      A&=&\$950.08
      \end{array}\)
   4. \(\begin{array}{rrl}
      \\ \\ \\ \\ \\ \\ \\
      A&=&\text{find}\hspace{0.25in} P=\$1500\hspace{0.25in} r=0.04\hspace{0.25in} n=2 \hspace{0.25in} t=7 \\ \\
      A&=&1500\left(1+\dfrac{0.04}{2}\right)^{14} \\ \\
      A&=&1500(1.02)^{14} \\ \\
      A&=&\$1979.22
      \end{array}\)
   5. \(\begin{array}{rrl}
      \\ \\ \\ \\ \\ \\ \\
      A&=&\text{find}\hspace{0.25in} P=\$900\hspace{0.25in} r=0.06\hspace{0.25in} n=2 \hspace{0.25in} t=5 \\ \\
      A&=&900\left(1+\dfrac{0.06}{2}\right)^{10} \\ \\
      A&=&900(1.03)^{10} \\ \\
      A&=&\$1209.52
      \end{array}\)
   6. \(\begin{array}{rrl}
      \\ \\ \\ \\ \\ \\ \\
      A&=&\text{find}\hspace{0.25in} P=\$950\hspace{0.25in} r=0.04\hspace{0.25in} n=2 \hspace{0.25in} t=12 \\ \\
      A&=&950\left(1+\dfrac{0.04}{2}\right)^{24} \\ \\
      A&=&950(1.02)^{24} \\ \\
      A&=&\$1528.02
      \end{array}\)
   7. \(\begin{array}{rrl}
      \\ \\ \\ \\ \\ \\ \\
      A&=&\text{find}\hspace{0.25in} P=\$2000\hspace{0.25in} r=0.05\hspace{0.25in} n=4 \hspace{0.25in} t=6 \\ \\
      A&=&2000\left(1+\dfrac{0.05}{4}\right)^{24} \\ \\
      A&=&2000(1.0125)^{24} \\ \\
      A&=&\$2694.70
      \end{array}\)
   8. \(\begin{array}{rrl}
      \\ \\ \\ \\ \\ \\ \\
      A&=&\text{find}\hspace{0.25in} P=\$2250\hspace{0.25in} r=0.04\hspace{0.25in} n=4 \hspace{0.25in} t=9 \\ \\
      A&=&2250\left(1+\dfrac{0.04}{4}\right)^{36} \\ \\
      A&=&2250(1.01)^{36} \\ \\
      A&=&\$3219.23
      \end{array}\)
   9. \(\begin{array}{rrl}
      \\ \\ \\ \\ \\ \\ \\
      A&=&\text{find}\hspace{0.25in} P=\$3500\hspace{0.25in} r=0.06\hspace{0.25in} n=4 \hspace{0.25in} t=12 \\ \\
      A&=&3500\left(1+\dfrac{0.06}{4}\right)^{48} \\ \\
      A&=&3500(1.015)^{48} \\ \\
      A&=&\$7152.17
      \end{array}\)
2. \(\begin{array}{rrl}
   \\ \\ \\ \\
   A&=&\$10,000\left(1+\dfrac{0.04}{4}\right)^{40} \\ \\
   A&=&\$10,000(1.01)^{40} \\ \\
   A&=&\$14,888.64
   \end{array}\)
3. \(\begin{array}{rrl}
   \\ \\ \\ \\
   A&=&\$27,500\left(1+\dfrac{0.06}{12}\right)^{12(9)} \\ \\
   A&=&\$27,500(1.005)^{108} \\ \\
   A&=&\$47,126.74
   \end{array}\)
4. \(\begin{array}{rrl}
   \\ \\ \\ \\
   A&=&\$55,000\left(1+\dfrac{0.10}{12}\right)^{18} \\ \\
   A&=&\$55,000(1.008\bar{3})^{18} \\ \\
   A&=&\$63,861.18
   \end{array}\)
5. \(\begin{array}{rrl}
   \\ \\ \\ \\ \\
   \$20,000&=&P\left(1+\dfrac{0.06}{2}\right)^{10} \\ \\
   P&=&\dfrac{\$20,000}{(1.03)^{10}} \\ \\
   P&=&\$14,881.88
   \end{array}\)
6. \(\begin{array}{rrl}
   \\ \\ \\ \\ \\
   \$4200&=&P\left(1+\dfrac{0.04}{4}\right)^{4(5)} \\ \\
   P&=&\dfrac{\$4200}{(1.01)^{20}} \\ \\
   P&=&\$3442.09
   \end{array}\)