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isabella
isabella asked in Education & ReferenceHomework Help · 6 years ago

I need help with a compound interest problem?

Update:

"You open one account with $5,000 that earns 6% annual interest, compounded monthly. You open another with $15,000 that earns 4% annual interest, compounded monthly. Compare the two balances over time. How long does it take for the $5,000 account to catch up with the $15,000 account?"

2 Answers

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  • MoneyMen
    Lv 7
    6 years ago

    55 years

  • hayharbr
    Lv 7
    6 years ago

    5000 (1 + 0.06/12)^(12x) = 15000 (1 + 0.04/12) ^(12x)

    Divide both sides by 5000

    (1 + 0.06/12)^(12x) = 3 (1 + 0.04/12) ^(12x)

    Log both sides

    12x log (201/200) = log 3 + 12x log (301/300)

    12x log (201/200) - 12x log (301/300) = log 3

    12x( log(201/200) - log (301/300)) = log 3

    x = log 3 ÷ [12 (log(201/200) - log (301/300)] or about 55 years IMO anyway, check and see if you agree

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