Question

In year, 2004, I put $20.00 into an account to save. This account annual interest fee is 0.002%. However, every 10th year the interest rate get doubled and is now 0.004%. After, the 10th year it goes back to the original interest rate of 0.002% annually. If I check the amount I know have in total included my principal of $20.00, in the year of 2021. What would the total amount be of putting it there

Answer 1

9514 1404 393

Answer:

  $20.01

Step-by-step explanation:

In 2004–2012, the interest rate is 0.002%. In 2013, it is 0.004%. In 2014–2021, the interest rate is 0.002%. That is, in the 18 years between 2004 and 2021 (inclusive), the interest rate is 0.002% for 17 of them. The effective account multiplier is ...

  (1.00002^17)(1.00004^1) = 1.00038006801

Then the account balance is ...

  $20 × 1.00038006801 ≈ $20.01

_____

Additional comment

The annual interest earned on $20.00 is $0.0004. If the account balance is rounded to the nearest cent annually, at the end of the 18 years, the balance will still be $20.00. Not enough interest is earned in one year to increase the balance above $20. At the end of the 18 years, the amount of interest earned is 0.76¢ (a fraction of a penny) only if there is no rounding in intervening years.