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The formula for calculating the amount of money returned for deposit money into a bank account or CD?

Suppose you deposit $20,000 for 3 years at a rate of 8%. If a bank compounds continuous, then the formula becomes simpler, that is

where e is a constant and equals approximately 2.7183. Now suppose, instead of knowing t, we know that the bank returned to us $25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t).

4 Answers

  • 1 decade ago
    Favorite Answer

    ok it sounds like you know how to do this, but just dont want to number crunch... anyway i'll start from the top.

    let's set up a formula that relates current value, future value, interest rate and time.

    25,000 = 20,000(1.08)^t

    first thing to do is get rid of that 20,000... so it becomes

    1.25 = 1.08^t

    take the log of each side and bring the t down.

    log1.25 = t log1.08

    so t = log1.25/log1.08

    t = 2.899435195 years

  • ?
    Lv 4
    4 years ago

    The formulation for the uniform sequence (A) back given a modern-day properly worth (P) is: A = P[(i(one million+i)^n]/[(one million+i)^n-one million] the place i is the useful interest cost, i =[one million+r/m]^m the place r is the nominal (annual) interest cost and m is the form of compounding sessions. n is the form of years. Sorry for changing extremely some the notation, yet it extremely is the way I found out it.

  • 1 decade ago

    formula for calculating the amount receivable when the amount is compounded annually....

    amount= p(1 + r/100)^t

    where p= principal

    r=rate of interest

    t=period for which the principal is left in a/c

    taking values of different variables



    taking log on both sides,

    log(1.25)=t log(1.08)


    =>t=2.9 yrs

  • 1 decade ago

    25,000 = 20,000e^(.08t)

    25,000/20,000 = e^(.08t)

    5/4 = e^(.08t)

    ln(5/4) =.08t

    You can take it from here. I gotta go.

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