{"id":2026,"date":"2021-12-02T19:40:32","date_gmt":"2021-12-03T00:40:32","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-11-6\/"},"modified":"2022-11-02T10:39:14","modified_gmt":"2022-11-02T14:39:14","slug":"answer-key-11-6","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-11-6\/","title":{"raw":"Answer Key 11.6","rendered":"Answer Key 11.6"},"content":{"raw":"
    \n \t
  1. [latex]\\phantom{a}[\/latex]\n
      \n \t
    1. [latex]A=\\text{find}\\hspace{0.25in} P=\\$500\\hspace{0.25in} r=0.04\\hspace{0.25in} n=1 \\hspace{0.25in} t=10[\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&500\\left(1+\\dfrac{0.04}{1}\\right)^{10} \\\\ \\\\\nA&=&500(1.04)^{10} \\\\ \\\\\nA&=&\\$740.12\n\\end{array}[\/latex]<\/li>\n \t
    2. [latex]A=\\text{find}\\hspace{0.25in} P=\\$600\\hspace{0.25in} r=0.06\\hspace{0.25in} n=1 \\hspace{0.25in} t=6[\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&600\\left(1+\\dfrac{0.06}{1}\\right)^6 \\\\ \\\\\nA&=&600(1.06)^6 \\\\ \\\\\nA&=&\\$851.11\n\\end{array}[\/latex]<\/li>\n \t
    3. [latex]A=\\text{find}\\hspace{0.25in} P=\\$750\\hspace{0.25in} r=0.03\\hspace{0.25in} n=1 \\hspace{0.25in} t=8[\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&750\\left(1+\\dfrac{0.03}{1}\\right)^8 \\\\ \\\\\nA&=&750(1.03)^8 \\\\ \\\\\nA&=&\\$950.08\n\\end{array}[\/latex]<\/li>\n \t
    4. [latex]A=\\text{find}\\hspace{0.25in} P=\\$1500\\hspace{0.25in} r=0.04\\hspace{0.25in} n=2 \\hspace{0.25in} t=7[\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&1500\\left(1+\\dfrac{0.04}{2}\\right)^{14} \\\\ \\\\\nA&=&1500(1.02)^{14} \\\\ \\\\\nA&=&\\$1979.22\n\\end{array}[\/latex]<\/li>\n \t
    5. [latex]A=\\text{find}\\hspace{0.25in} P=\\$900\\hspace{0.25in} r=0.06\\hspace{0.25in} n=2 \\hspace{0.25in} t=5[\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&900\\left(1+\\dfrac{0.06}{2}\\right)^{10} \\\\ \\\\\nA&=&900(1.03)^{10} \\\\ \\\\\nA&=&\\$1209.52\n\\end{array}[\/latex]<\/li>\n \t
    6. [latex]A=\\text{find}\\hspace{0.25in} P=\\$950\\hspace{0.25in} r=0.04\\hspace{0.25in} n=2 \\hspace{0.25in} t=12[\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&950\\left(1+\\dfrac{0.04}{2}\\right)^{24} \\\\ \\\\\nA&=&950(1.02)^{24} \\\\ \\\\\nA&=&\\$1528.02\n\\end{array}[\/latex]<\/li>\n \t
    7. [latex]A=\\text{find}\\hspace{0.25in} P=\\$2000\\hspace{0.25in} r=0.05\\hspace{0.25in} n=4 \\hspace{0.25in} t=6[\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&2000\\left(1+\\dfrac{0.05}{4}\\right)^{24} \\\\ \\\\\nA&=&2000(1.0125)^{24} \\\\ \\\\\nA&=&\\$2694.70\n\\end{array}[\/latex]<\/li>\n \t
    8. [latex]A=\\text{find}\\hspace{0.25in} P=\\$2250\\hspace{0.25in} r=0.04\\hspace{0.25in} n=4 \\hspace{0.25in} t=9 [\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&2250\\left(1+\\dfrac{0.04}{4}\\right)^{36} \\\\ \\\\\nA&=&2250(1.01)^{36} \\\\ \\\\\nA&=&\\$3219.23\n\\end{array}[\/latex]<\/li>\n \t
    9. [latex]A=\\text{find}\\hspace{0.25in} P=\\$3500\\hspace{0.25in} r=0.06\\hspace{0.25in} n=4 \\hspace{0.25in} t=12 [\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&3500\\left(1+\\dfrac{0.06}{4}\\right)^{48} \\\\ \\\\\nA&=&3500(1.015)^{48} \\\\ \\\\\nA&=&\\$7152.17\n\\end{array}[\/latex]<\/li>\n<\/ol>\n<\/li>\n \t
    10. [latex]A=\\$10,000\\left(1+\\dfrac{0.04}{4}\\right)^{40} [\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&\\$10,000(1.01)^{40} \\\\ \\\\\nA&=&\\$14,888.64\n\\end{array}[\/latex]<\/li>\n \t
    11. [latex]A=\\$27,500\\left(1+\\dfrac{0.06}{12}\\right)^{12(9)}[\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&\\$27,500(1.005)^{108} \\\\ \\\\\nA&=&\\$47,126.74\n\\end{array}[\/latex]<\/li>\n \t
    12. [latex]A=\\$55,000\\left(1+\\dfrac{0.10}{12}\\right)^{18} [\/latex]\n[latex]\\begin{array}[t]{rrl}\nA&=&\\$55,000(1.008\\bar{3})^{18} \\\\ \\\\\nA&=&\\$63,861.18\n\\end{array}[\/latex]<\/li>\n \t
    13. [latex]\\$20,000=P\\left(1+\\dfrac{0.06}{2}\\right)^{10} [\/latex]\n[latex]\\begin{array}[t]{rrl}\nP&=&\\dfrac{\\$20,000}{(1.03)^{10}} \\\\ \\\\\nP&=&\\$14,881.88\n\\end{array}[\/latex]<\/li>\n \t
    14. [latex]\\$4200=P\\left(1+\\dfrac{0.04}{4}\\right)^{4(5)} [\/latex]\n[latex]\\begin{array}[t]{rrl}\nP&=&\\dfrac{\\$4200}{(1.01)^{20}} \\\\ \\\\\nP&=&\\$3442.09\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
        \n
      1. [latex]\\phantom{a}[\/latex]\n
          \n
        1. [latex]A=\\text{find}\\hspace{0.25in} P=\\$500\\hspace{0.25in} r=0.04\\hspace{0.25in} n=1 \\hspace{0.25in} t=10[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&500\\left(1+\\dfrac{0.04}{1}\\right)^{10} \\\\ \\\\ A&=&500(1.04)^{10} \\\\ \\\\ A&=&\\$740.12 \\end{array}[\/latex]<\/li>\n
        2. [latex]A=\\text{find}\\hspace{0.25in} P=\\$600\\hspace{0.25in} r=0.06\\hspace{0.25in} n=1 \\hspace{0.25in} t=6[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&600\\left(1+\\dfrac{0.06}{1}\\right)^6 \\\\ \\\\ A&=&600(1.06)^6 \\\\ \\\\ A&=&\\$851.11 \\end{array}[\/latex]<\/li>\n
        3. [latex]A=\\text{find}\\hspace{0.25in} P=\\$750\\hspace{0.25in} r=0.03\\hspace{0.25in} n=1 \\hspace{0.25in} t=8[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&750\\left(1+\\dfrac{0.03}{1}\\right)^8 \\\\ \\\\ A&=&750(1.03)^8 \\\\ \\\\ A&=&\\$950.08 \\end{array}[\/latex]<\/li>\n
        4. [latex]A=\\text{find}\\hspace{0.25in} P=\\$1500\\hspace{0.25in} r=0.04\\hspace{0.25in} n=2 \\hspace{0.25in} t=7[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&1500\\left(1+\\dfrac{0.04}{2}\\right)^{14} \\\\ \\\\ A&=&1500(1.02)^{14} \\\\ \\\\ A&=&\\$1979.22 \\end{array}[\/latex]<\/li>\n
        5. [latex]A=\\text{find}\\hspace{0.25in} P=\\$900\\hspace{0.25in} r=0.06\\hspace{0.25in} n=2 \\hspace{0.25in} t=5[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&900\\left(1+\\dfrac{0.06}{2}\\right)^{10} \\\\ \\\\ A&=&900(1.03)^{10} \\\\ \\\\ A&=&\\$1209.52 \\end{array}[\/latex]<\/li>\n
        6. [latex]A=\\text{find}\\hspace{0.25in} P=\\$950\\hspace{0.25in} r=0.04\\hspace{0.25in} n=2 \\hspace{0.25in} t=12[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&950\\left(1+\\dfrac{0.04}{2}\\right)^{24} \\\\ \\\\ A&=&950(1.02)^{24} \\\\ \\\\ A&=&\\$1528.02 \\end{array}[\/latex]<\/li>\n
        7. [latex]A=\\text{find}\\hspace{0.25in} P=\\$2000\\hspace{0.25in} r=0.05\\hspace{0.25in} n=4 \\hspace{0.25in} t=6[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&2000\\left(1+\\dfrac{0.05}{4}\\right)^{24} \\\\ \\\\ A&=&2000(1.0125)^{24} \\\\ \\\\ A&=&\\$2694.70 \\end{array}[\/latex]<\/li>\n
        8. [latex]A=\\text{find}\\hspace{0.25in} P=\\$2250\\hspace{0.25in} r=0.04\\hspace{0.25in} n=4 \\hspace{0.25in} t=9[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&2250\\left(1+\\dfrac{0.04}{4}\\right)^{36} \\\\ \\\\ A&=&2250(1.01)^{36} \\\\ \\\\ A&=&\\$3219.23 \\end{array}[\/latex]<\/li>\n
        9. [latex]A=\\text{find}\\hspace{0.25in} P=\\$3500\\hspace{0.25in} r=0.06\\hspace{0.25in} n=4 \\hspace{0.25in} t=12[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&3500\\left(1+\\dfrac{0.06}{4}\\right)^{48} \\\\ \\\\ A&=&3500(1.015)^{48} \\\\ \\\\ A&=&\\$7152.17 \\end{array}[\/latex]<\/li>\n<\/ol>\n<\/li>\n
        10. [latex]A=\\$10,000\\left(1+\\dfrac{0.04}{4}\\right)^{40}[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&\\$10,000(1.01)^{40} \\\\ \\\\ A&=&\\$14,888.64 \\end{array}[\/latex]<\/li>\n
        11. [latex]A=\\$27,500\\left(1+\\dfrac{0.06}{12}\\right)^{12(9)}[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&\\$27,500(1.005)^{108} \\\\ \\\\ A&=&\\$47,126.74 \\end{array}[\/latex]<\/li>\n
        12. [latex]A=\\$55,000\\left(1+\\dfrac{0.10}{12}\\right)^{18}[\/latex]
          \n[latex]\\begin{array}[t]{rrl} A&=&\\$55,000(1.008\\bar{3})^{18} \\\\ \\\\ A&=&\\$63,861.18 \\end{array}[\/latex]<\/li>\n
        13. [latex]\\$20,000=P\\left(1+\\dfrac{0.06}{2}\\right)^{10}[\/latex]
          \n[latex]\\begin{array}[t]{rrl} P&=&\\dfrac{\\$20,000}{(1.03)^{10}} \\\\ \\\\ P&=&\\$14,881.88 \\end{array}[\/latex]<\/li>\n
        14. [latex]\\$4200=P\\left(1+\\dfrac{0.04}{4}\\right)^{4(5)}[\/latex]
          \n[latex]\\begin{array}[t]{rrl} P&=&\\dfrac{\\$4200}{(1.01)^{20}} \\\\ \\\\ P&=&\\$3442.09 \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":112,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-2026","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2026","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2026\/revisions"}],"predecessor-version":[{"id":2027,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2026\/revisions\/2027"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2026\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=2026"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=2026"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=2026"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=2026"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}