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A bank offers an interest rate of r compounded n times per year. The formula for the amount of money, A, in an account at the end of t years, is:
A = P ( 1 + r ) nt
                         n
where P is the amount of money in the account at the beginning of the year (assuming no deposits or withdrawals).

A) If at the beginning of the year Joe had $1,000 in an account with 2% interest compounded semiannually, how much money would he have in the account at the end of the year? Show your work or provide an explanation for your answer.

B) The effective interest rate, R, is the percent increase in the account over one year. What is the effective interest rate for Joe's account? (Do not round your answer.) Show your work or provide an explanation for your answer.

C) Joe had x dollars in his account at the beginning of the year. Describe how to determine the amount of money Joe would have in his account after 1 year using the effective rate you found above.

Materials/Resources:

  • Calculator
    HSPA Mathematics Reference Sheet

Techniques for PAT Scoring:
See item-specific sample response and scoring rubric B0706-002R for this PAT.

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