Compound Interest and Geometrical Sequences

Question

$1000 has been in a savings account where it has earned 5% interest per year from 1799-2014. How much money is in the account?

 

Please include all steps and show how you get from the compound interest formula to the sum of a geometric sequence formula. Thanks!

Answer 1

“$1000 has been in a savings account where it has earned 5% interest per year from 1799-2014. How much money is in the account?

Please include all steps and show how you get from the compound interest formula to the sum of a geometric sequence formula.”

You can’t use geometric series to solve compound interest problems, as I explained here: http://www.wyzant.com/resources/answers/30303/geometric_series_and_sequences_questions_help_updated.

The Compound Interest Formula is:
A = P(1 + r/n)^(nt), where
t is the number of time units,
n is the number of times IN EACH TIME UNIT that interest is calculated and added to the account,
r is the interest rate PER TIME UNIT,
P is the original amount called the Principal, and
A is the amount in the account.

For this problem:
t = 2014 - 1799 = 215 years
n = 1 times per year interest is calculated
r = 5%/year = 0.05/year
P = $1,000

A = 1000(1 + 0.05/1)^((1)215)

Now simplify and use your calculator.

Answer 2

2014 - 1799 = 215 years that $1000 was in saving account.

 

 

 Compound interest of 5% for 215 years

 

   1000 ( 1 + 0.05) ^215 = 35, 950,000 

  

    Problem stated " earned 5% interest per year", means that average interest  rate earned was 5%

 

      in which case

 

     The money at year 2014 will be

 

       1000 ( 1 +  215 ( 0.05) = 11,750