Question

Ava opens an account with $400. She deposits $200/month for 20 years. The interest rate is 2.15%. How much interest will she have earned after 20 years?
a. $61,243.59




b. $48,800




c. 12,443.59




d. None of the above.

Answer 1

Answer:

  d.  None of the above

Step-by-step explanation:

We assume the sequence of deposits is ...

  month 0: $400

  month 1: $200

  month 2: $200

...

  month 240: $200 . . . . accumulated interest is determined at this point

That is, no interest is earned on the last deposit.

_____

The value of the initial $400 deposit after 20 years at 2.15% interest compounded monthly is ...

  $400×(1 +.0215/12)^(12×20) = $400×1.536666 ≈ $614.67

The value of the $200 annuity at the same interest rate is ...

  $200((1 +.0215/12)^(12×20) -1)/(.0215/12) = $200×299.534612 ≈ $59,906.92

So, the total account value is ...

  $614.67 +59,906.92 = $60521.59

The total amount deposited was ...

  $400 +$200×240 = $48,400

The interest earned is the difference between the account value and the total of deposits:

  $60,521.59 -48,400 = $12,121.59 . . . . interest earned

This value does not match any numerical answer choice, so we conclude the appropriate answer is ...

   None of the above