Please help with interest rate question!?

Martina deposited $4000 into an account with 3% interest, compounded semiannually. Assuming that no withdrawals are made, how much will she have in the account after 7 years?

Do not round any intermediate computations, and round your answer to the nearest cent.

3 Answers

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  • ?
    Lv 7
    1 decade ago
    Favorite Answer

    ... An = A0 (1 + r/2)^(2y) ← semiannually = 2 times per year

    or An = 4000 (1 + .03/2)^(2*7)

    or An = 4000 (1.015)^(14)

    or An = $ 4,927.02

  • Anonymous
    1 decade ago

    It depends. Is the 3% interest rate a 6 month interest rate? Or is it a one year interest rate? Interest is being compounded every 6 months, so we need to work in a 6 month interest rate.

    If 3% is a 6 month interest rate....

    The account will be credited with interest for 7 years, or 14 six month periods.

    Future Value = 4000(1+i)^n = 4000(1.03)^14 = $6050.36

    If 3% is a one year interest rate... then it is a little trickier:

    Using a 3% nominal annual rate, then we need to compute a six month interest rate.

    Since a 6 month period is exactly one half of a year, the 6 month rate is exactly one half of 3% or 1.5%

    Future Value = 4000(1+i)^n = 4000(1.015)^14 = $4927.02

  • 1 decade ago

    Year 1 = 4000

    Year 2 = 4120

    Year 3 = 4243.6

    Year 4 = 4370.91

    Year 5 = 4502.04

    Year 6 = 4637.01

    Year 7 = 4776.21

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