Question

Madeline received $300 for her birthday. She deposits it into a savings account with an interest rate of 2.45%. She makes monthly deposits of $150. How much interest will she have earned after 8 years?
a. $16,257.57




b. $1,587.57




c. $14,700




d. None of the above.

Answer 1

Answer:

  b.  $1,587.57

Step-by-step explanation:

A financial calculator will tell you the value of Madeline's account after  8 years will be $16,287.57. In that time, she will have deposited ...

  $300 +96×150 = $14,700

The interest earned is the difference between her account balance and the amount she deposited:

  $16,287.57 -14,700 = $1,587.57 . . . interest earned

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Account value calculation

The future value of the initial $300 deposit after 8 years is ...

  A = P(1 +r/n)^(nt)

for principal P earning annual rate r compounded n times per year for t years.

  A = $300(1 +0.0245/12)^(12·8) ≈ $364.89

The future value of the sum of $150 deposits monthly (at the beginning of the month) will be ...

  A = $150((1+r/n)^(nt) -1)(1 +n/r) = $15,922.68

So, the total value of Madeline's account in 8 years is ...

  $364.89 +15,922.68 = $16,287.57

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Comment on account value

In problems of this nature, it is always necessary to determine when the deposits are made relative to when the account value is measured. Here, we assume the $300 deposit is immediate, and its value is measured 8 years hence.

The monthly deposits are not described in that detail. In order to get any of the numbers in the answer list, we need to assume the deposits are at the beginning of the month. If we assume they are at the end of the month, the amount of interest is reduced by about $33.18, the last month's interest.