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Math Help - Problem with saving account

  1. #1
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    Problem with saving account

    You save 20 000 on a savings account at the end of each year for 9 years. The annual interest rate is 3%.
    a) How much is the total amount immediately after the last deposit?

    b) How much is the total amount 5 years after the last deposit?
    You save an amount K on a savings account at the end of each year for 9 years.The annual interest rate is 3%.

    c) How much is the yearly savings amount if the total amount 5years after the last deposit is 300 000?
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  2. #2
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    Hello, Mariana!

    These involve an Annuity and then Compound Interest.


    You save $20 000 in a savings account at the end of each year for 9 years.
    The annual interest rate is 3%.
    a) How much is the total amount immediately after the last deposit?
    . . . . . . . . . . . . . . . . . . .(1 + i)^n - 1
    Annuity formula: . A .= .D ---------------
    . . . . . . . . . . . . . . . . . . . . . . i

    where D = periodic deposit
    . . . . . i = periodic interest rate
    . . . . .n = number of periods
    . . . . .A = final amount


    We have: D = 20,000, i = 0.03, n = 9

    . . . . . . . . . . . . . . . . . . 1.03^
    9 - 1
    Therefore: . A .= .20,000 ------------- . . $203,182.12
    . . . . . . . . . . . . . . . . . . . . 0.03



    b) You save an amount K on a savings account at the end of each year for 9 years.
    The annual interest rate is 3%.
    How much is the total amount 5 years after the last deposit?
    We deposit K dollars each year for 9 years at 3%

    . . . . . . . . . . . . . . . . . . . . . . 1.03^
    9 - 1
    At the end of 9 years: . A .= .K ------------- . .10.1591K
    . . . . . . . . . . . . . . . . . . . . . . . . 0.03


    This amount is left in the account for another 5 years.

    . . Its value will be: .10.1581K (1.03)^
    5 . .11.776K


    c) How much is the yearly savings amount if the total amount 5 years
    after the last deposit is $300 000?
    If the above value is $300,000: .11.776K .= .300,000 . . K . .$25,475.54


    Drat . . . The deposits are made at the end of each year.
    Are all my answers wrong?
    If they are, would someone correct them . . . please?
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