Question

Colleen is 15 years from retiring. She opens an account at the Savings Bank. She plans to deposit

Answer 1

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Answer:

  a) $169,234.59

  b) $19,234.59

Step-by-step explanation:

The first question you must answer is whether Colleen will earn interest on her first deposit in the first year. That is, does she deposit the money at the first of the year or the end of the year?

The usual "annuity" formula assumes the deposit is at the end of the year, so no interest at all is earned on the last deposit made. If the deposit is at the first of the year, an "annuity due" formula is used, that multiplies the entire ending account value by the annual multiplier, 1.017 in this case.

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a) Assuming an "annuity", the formula is ...

  A = P((1 +r)^t -1)/r . . . . . for annual compounding at rate r for t years

  A = $10,000(1.017^15 -1)/0.017 = $169,234.59 . . . . ending balance

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b) Colleen has made 15 deposits of $10,000, for a total of $150,000, so the amount of interest earned is ...

  $169,234.59 -150,000 = $19,234.59 . . . . interest earned