You invested in a 3-month certificate of deposit at your bank. Your investment was $1,902, and at the end of the term you will receive $2,17

You invested in a 3-month certificate of deposit at your bank. Your investment was $1,902, and at the end of the term you will receive $2,178.
a. What is the holding period return (HPR) on your investment? (Round your answer to 2 decimal places.)
b. What is the annual percentage rate (APR)? (Round your answer to 2 decimal places.)
c. What is the effective annual rate (EAR)? (Round your answer to 2 decimal places.)

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  1. Answer and Explanation:

    The computation is shown below:

    a. Holding period return would be

    = Income + (End of Period Value – Initial Value) ÷ Initial Value

    = 0 +($2,178 – $1,902) ÷ $1,902

    = 0 + $276 ÷ $1,902


    = 14.51%

    b. The annual percentage rate is

    For 3 months, the rate is 14.51%

    Now

    For 12 months, it is

    = 14.51% ÷ 3 ×  12

    = 14.51 % × 4

    = 58.04%

    c. The effective annual rate is

    = ( 1 + r ÷ m)^m – 1

    = (1 + 58.04% ÷ 4)^4 – 1

    = (1 + 0.5804 ÷ 4)^4 – 1

    = (1 + 0.1451)^4 – 1

    = (1.1451)^4 – 1

    = 1.719387079 – 1

    = 0.719387079 or 71.94%

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