You put $10000 in an account earning 5%. After 3 years, you make another deposit into the same account. Four years later (7 years after init

You put $10000 in an account earning 5%. After 3 years, you make another deposit into the same account. Four years later (7 years after initial $10000) the account balance is $20000. What was the amount of the deposit at the end of year 3

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  1. Answer:

    money deposited after end of 3rd year is $4877.75  

    Explanation:

    given data

    initial amount  = $10000

    rate = 5%

    time = 3 year

    after 7 year account balance = $20000

    solution

    we consider here money deposited after end of 3rd year is = x

    first we get here compounded amount after 3 years as

    compounded amount = initial amount × [tex](1+r)^{t}[/tex]    …………….1

    compounded amount = 10000 × [tex](1+0.05)^{3}[/tex]

    compounded amount = $11576.25

    so at 7 year account balance is

    account balance = ( compounded amount + x )  × [tex](1+r)^{t}[/tex] ………………..2

    $20000  = ( $11576.25 + x ) × [tex](1+0.5)^{4}[/tex]  

    solve it we get

    x =  $4877.75  

    so money deposited after end of 3rd year is $4877.75  

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