3 part question on Intrest Earned

Question

Beginning in​ January, a person plans to deposit ​$1000 at the end of each month into an account earning 9% compounded monthly. Each year taxes must be paid on the interest earned during that year. Find the interest earned during each year for the first 3 years.

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Part 1

The interest earned during the first year is

​$507.59

​(Round to the nearest cent as​ needed.)

Part 2

The interest earned during the second year is

​$1680.88

​(Round to the nearest cent as​ needed.)

Part 3

The interest earned during the third year is _____?

Please provide a step by step explaination of each part.

Answer 1

First of all, when interest is compounded monthly, the interest is paid on the balance on the first day of the month.

Secondly, the monthly interest is 0.09/12 = 0.0075 (aka 0.75%).

At the end of the first month (January) the deposit is made but no interest is earned because the deposit is made on the last day of the month. So the balance is 1000 on day 1 of February. The Feb interest is 1000(0.0075) = $7.50. Combined with the Feb end-of-the-month deposit we get a month-end balance of $2007.50. The interest for March is then (2007.50)(0.0075) = $15.06 and the process continues:

Month Beginning Balance Interest Deposit Month-end Balance

Jan 0 0 1000 1000.00

Feb 1000 7.50 1000 2007.50

Mar 2007.50 15.06 1000 3022.56

Apr 3022,56 22.67 1000 4045.23

May 4045.23 30.34 1000 5075.56

Jun 5075.56 38.07 1000 6113.63

etc, etc

Once the table above is complete, you can add up all the interest to get the yearly total.

If you are paying taxes out of the balance, you would need to subtract the tax payment from your balance at the end of the year.

If you have Excel, this table is easy to generate.

If you have a financial calculator, this becomes a TVM Solver problem. I recommend you look at you tube to see how to use it.