Sum of Geometric progression?

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A man deposits $200 at the beginning of every year into a bank account at a compund interest rate of 3%per annum. Find out how much he has at the end of 10th year to the nearest dollar?



I honestly don't quite understand the part about "depositing $200 every year".



How do you go about solving this?






sequences-and-series geometric-progressions







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    up vote
    2
    down vote

    favorite












    A man deposits $200 at the beginning of every year into a bank account at a compund interest rate of 3%per annum. Find out how much he has at the end of 10th year to the nearest dollar?



    I honestly don't quite understand the part about "depositing $200 every year".



    How do you go about solving this?






    sequences-and-series geometric-progressions







    share|cite|improve this question

























      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      A man deposits $200 at the beginning of every year into a bank account at a compund interest rate of 3%per annum. Find out how much he has at the end of 10th year to the nearest dollar?



      I honestly don't quite understand the part about "depositing $200 every year".



      How do you go about solving this?






      sequences-and-series geometric-progressions







      share|cite|improve this question















      A man deposits $200 at the beginning of every year into a bank account at a compund interest rate of 3%per annum. Find out how much he has at the end of 10th year to the nearest dollar?



      I honestly don't quite understand the part about "depositing $200 every year".



      How do you go about solving this?






      sequences-and-series geometric-progressions




      sequences-and-series geometric-progressions






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




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      edited 4 hours ago

























      asked 4 hours ago









      Henias

      234




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          2 Answers
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          The first $$200$ compounds for $10$ years
          the next year he deposits another $$200$ into the account, and that will compound for $9$ more years.



          After 10 years he has:



          $200(1.03)^10 + 200(1.03)^9 + cdots + 200(1.03)$



          And how would you sum that up?






          share|cite|improve this answer



























            up vote
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            At the end of the first year it's going to be $200 cdot 1.03$;
            at the end of the second year it's going to be $(200 cdot 1.03 + 200) cdot 1.03=200 cdot (1.03+1.03^2)$;
            at the end of the third year we will have $200 cdot (1.03+1.03^2+1.03^3)$.
            Do you see the pattern?






            share|cite|improve this answer




















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              2 Answers
              2






              active

              oldest

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              2 Answers
              2






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes








              up vote
              4
              down vote



              accepted










              The first $$200$ compounds for $10$ years
              the next year he deposits another $$200$ into the account, and that will compound for $9$ more years.



              After 10 years he has:



              $200(1.03)^10 + 200(1.03)^9 + cdots + 200(1.03)$



              And how would you sum that up?






              share|cite|improve this answer
























                up vote
                4
                down vote



                accepted










                The first $$200$ compounds for $10$ years
                the next year he deposits another $$200$ into the account, and that will compound for $9$ more years.



                After 10 years he has:



                $200(1.03)^10 + 200(1.03)^9 + cdots + 200(1.03)$



                And how would you sum that up?






                share|cite|improve this answer






















                  up vote
                  4
                  down vote



                  accepted







                  up vote
                  4
                  down vote



                  accepted






                  The first $$200$ compounds for $10$ years
                  the next year he deposits another $$200$ into the account, and that will compound for $9$ more years.



                  After 10 years he has:



                  $200(1.03)^10 + 200(1.03)^9 + cdots + 200(1.03)$



                  And how would you sum that up?






                  share|cite|improve this answer












                  The first $$200$ compounds for $10$ years
                  the next year he deposits another $$200$ into the account, and that will compound for $9$ more years.



                  After 10 years he has:



                  $200(1.03)^10 + 200(1.03)^9 + cdots + 200(1.03)$



                  And how would you sum that up?







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 4 hours ago









                  Doug M

                  41.4k31752




                  41.4k31752




















                      up vote
                      3
                      down vote













                      At the end of the first year it's going to be $200 cdot 1.03$;
                      at the end of the second year it's going to be $(200 cdot 1.03 + 200) cdot 1.03=200 cdot (1.03+1.03^2)$;
                      at the end of the third year we will have $200 cdot (1.03+1.03^2+1.03^3)$.
                      Do you see the pattern?






                      share|cite|improve this answer
























                        up vote
                        3
                        down vote













                        At the end of the first year it's going to be $200 cdot 1.03$;
                        at the end of the second year it's going to be $(200 cdot 1.03 + 200) cdot 1.03=200 cdot (1.03+1.03^2)$;
                        at the end of the third year we will have $200 cdot (1.03+1.03^2+1.03^3)$.
                        Do you see the pattern?






                        share|cite|improve this answer






















                          up vote
                          3
                          down vote










                          up vote
                          3
                          down vote









                          At the end of the first year it's going to be $200 cdot 1.03$;
                          at the end of the second year it's going to be $(200 cdot 1.03 + 200) cdot 1.03=200 cdot (1.03+1.03^2)$;
                          at the end of the third year we will have $200 cdot (1.03+1.03^2+1.03^3)$.
                          Do you see the pattern?






                          share|cite|improve this answer












                          At the end of the first year it's going to be $200 cdot 1.03$;
                          at the end of the second year it's going to be $(200 cdot 1.03 + 200) cdot 1.03=200 cdot (1.03+1.03^2)$;
                          at the end of the third year we will have $200 cdot (1.03+1.03^2+1.03^3)$.
                          Do you see the pattern?







                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered 4 hours ago









                          Vasya

                          3,0491514




                          3,0491514



























                               

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