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You invest​ $1,000 at a variable rate of interest. Initially the rate is​ 4% compounded annually for the first​ year, and the rate increases oneminushalf of one percent annually for five years​ (year two's rate is​ 4.5%, year​ three's rate is​ 5.0%, etc.). How much will you have in the account after five​ years?

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Answer:

You will have $1,276 in your account after 5 years.

Explanation:

The interest rate information is given for 6 years but the question is only asking the amount after 5 years, so I only make the calculation for that.

Rate in:

  • first year: 4%
  • second year: 4.5%
  • third year: 5%
  • fourth year: 5.5%
  • fifth year: 6%

Assuming interest in compounded throughout five years, the amount you will have in your account is:

FV = 1,000 * (1 + 0.04) * (1 + 0.045) * (1 + 0.05)*  (1 + 0.055) * (1 + 0.06) = $1,276

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