SOLUTION: Beginning in​ January, a person plans to deposit ​$10 at the end of each month into an account earning 6​% compounded monthly. Each year taxes must be paid on the interest ea

Algebra ->  Finance -> SOLUTION: Beginning in​ January, a person plans to deposit ​$10 at the end of each month into an account earning 6​% compounded monthly. Each year taxes must be paid on the interest ea      Log On


   

Question 1177408: Beginning in​ January, a person plans to deposit ​$10 at the end of each month into an account earning 6​% 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.

Homework question from Hans Beauvoir
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
**Year 1**
* **Monthly interest rate:** 6% annual rate compounded monthly means a monthly rate of 0.06 / 12 = 0.005.
* **Month 1:** $10 deposit earns no interest in the first month.
* **Month 2:** $10 (previous deposit) earns $10 * 0.005 = $0.05 interest. A new $10 deposit is made. The balance is $20.05.
* **Month 3:** $20.05 (previous balance) earns $20.05 * 0.005 = $0.10 interest. A new $10 deposit is made. The balance is $30.15.
We continue this process for 12 months. Here are the results:
| Month | Starting Balance | Interest Earned |
|---|---|---|
| 1 | $0.00 | $0.00 |
| 2 | $10.00 | $0.05 |
| 3 | $20.05 | $0.10 |
| 4 | $30.15 | $0.15 |
| 5 | $40.30 | $0.20 |
| 6 | $50.50 | $0.25 |
| 7 | $60.75 | $0.30 |
| 8 | $71.05 | $0.35 |
| 9 | $81.40 | $0.41 |
| 10 | $91.81 | $0.46 |
| 11 | $102.27 | $0.51 |
| 12 | $112.78 | $0.56 |
**Total Interest for Year 1:** $3.94
**Year 2**
We start with the ending balance of Year 1 ($112.78) and repeat the process.
| Month | Starting Balance | Interest Earned |
|---|---|---|
| 13 | $112.78 | $0.56 |
| 14 | $123.34 | $0.62 |
| 15 | $133.96 | $0.67 |
| 16 | $144.63 | $0.72 |
| 17 | $155.35 | $0.78 |
| 18 | $166.13 | $0.83 |
| 19 | $176.96 | $0.88 |
| 20 | $187.84 | $0.94 |
| 21 | $198.78 | $0.99 |
| 22 | $209.77 | $1.05 |
| 23 | $220.82 | $1.10 |
| 24 | $231.92 | $1.16 |
**Total Interest for Year 2:** $10.28
**Year 3**
Repeat with the ending balance of Year 2 ($231.92).
| Month | Starting Balance | Interest Earned |
|---|---|---|
| 25 | $231.92 | $1.16 |
| 26 | $243.08 | $1.22 |
| 27 | $254.30 | $1.27 |
| 28 | $265.57 | $1.33 |
| 29 | $276.90 | $1.38 |
| 30 | $288.28 | $1.44 |
| 31 | $299.72 | $1.50 |
| 32 | $311.22 | $1.56 |
| 33 | $322.78 | $1.61 |
| 34 | $334.39 | $1.67 |
| 35 | $346.06 | $1.73 |
| 36 | $357.79 | $1.79 |
**Total Interest for Year 3:** $18.66
**Summary of Interest Earned**
* Year 1: $3.94
* Year 2: $10.28
* Year 3: $18.66