SOLUTION: On the first day of the year, Mr. John deposits 1,000 dollars in a bank at interest rate of 8% per year, compounded annually. He withdraws 80 dollars at the end of first year, 90 d

Question 1183015: On the first day of the year, Mr. John deposits 1,000 dollars in a bank at interest rate of 8% per year, compounded annually. He withdraws 80 dollars at the end of first year, 90 dollars at the end of second year, and the remaining at the third year. How much does he withdraw at the end of the third year?

--Please help me on this ma'am and sir. I really want to learn. Thanks a lot!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

the sequence is as follows:

beginning of first year
1000 is deposited into the account.
end of first year
1000 * 1.08 = 1080 - 80 = 1000
end of second year
1000 * 1.08 = 108 - 90 = 990
end of third year
990 * 1.08 = 1069.2

the money is deposited at the beginning of the first year.
at the end of the first year, the money has earned 8% interest to make a remaining balance of 1000 * 1.08 = 1080.
80 dollars is then withdrawn to make a remaining balance of 1000 in the account.
this is the amount remaining in the account at the end of the first year, which is the same time point as the beginning of the second year.
at the end of the second year, the remaining balance at the end of the first year earns another 8% interest to make it equal to 1000 * 1.08 = 1080.
90 dollars is then withdrawn from the account, making the remaining balance equal to 990 at the end of the second year.
at the end of the third year, the remaining balance of 990 earns 8% interest to make it equal to 990 * 1.08 = 1069.2.
this is the remaining balance at the end of the third year.
that is the amount that is then withdrawn.

the following spreadsheet shows the year by year transactions.

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