Sumaya is considering investing $8500 into the bank. Bank A offers 2.25% interest rate compounded semiannually. Bank B offers 1.75% interest

Question

Sumaya is considering investing $8500 into the bank. Bank A offers 2.25% interest rate compounded semiannually. Bank B offers 1.75% interest compounded monthly.
She is planning on leaving the money in the account for 5 years until she goes to college.

Which bank should Sumaya go with and how much more will she make at that bank in the five years?

A. Bank A – she will make $1341.56 more

B. Bank B – she will make $1341.56 more.

C. Bank A – she will make $230.02 more.

D. Bank B – she will make $230.02 more.

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Khánh Gia 6 months 2021-08-04T08:51:20+00:00 1 Answers 19 views 0

Answers ( )

    0
    2021-08-04T08:52:27+00:00

    9514 1404 393

    Answer:

      C. Bank A – she will make $230.02 more.

    Step-by-step explanation:

    The account balance at each bank can be computed from …

      A = P(1 +r/n)^(nt)

    where principal P is invested at annual rate r compounded n times per year for t years.

    Bank A

    Sumaya’s balance after 5 years will be …

      A = 8500(1 + 0.0225/2)^(2·5) = 9506.14

    Bank B

    Sumaya’s balance after 5 years will be …

      A = 8500(1 +0.0175/12)^(12·5) = 9276.67

    __

    The balance at Bank A is larger by …

      9506.14 -9276.67 = 229.47

    The closest answer choice is …

      C. Bank A – she will make $230.02 more

    _____

    Comment on the discrepancy

    The difference between the offered answer choices and the values computed here arise from the use of rounding in intermediate calculations. We did no rounding until the final answer. The offered choices seem to be rounded to about 8 digits, possibly the consequence of using an inadequate calculator.

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