Compound Interest please help?!?

1)An investment account earns 6 % compounded monthly. An initial investment of $ 13000 (present value) grows to $ 32500 (future value) in t years. Find t.

2)Suppose we invest $ 500.How long will it take for our account to grow to $ 3500 if it is invested at an annual rate of 8 % compounded continuously?

3)Suppose we deposit $ 12000 into an investment account.What annual rate of interest is needed in order for the investment account to double in 10 years if interest is compounded continuously?

4)We deposit $ 13000 into an account earning 7 % interest compounded semiannually. How many years will it take for the account to grow to $ 32500?

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  • 1 decade ago
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    A = P·(1 + r/n)^(nt)

    P = principal amount

    r = annual nominal interest rate

    n = number of times the interest is compounded per year

    t = number of years

    A = amount after time t

    32500 = 13000 · [1 + 0.06/12]^(12t)

    ln(32500/13000) = 12t ln(1.005)

    t = ln(2.5) / [ 12 ln(1.005) ]

    t ≈ 15.3 years

    Answer: ≈ 15.3 years

    3500 = 500 · e^.08t

    ln(3500/500) = 0.08t

    t = ln(3500/500) / 0.08

    t ≈ 24.3 years

    Answer: t ≈ 24.3 years

    24000 = 12000 · e^10i

    ln(2) = 10i

    i = ln(2)/10

    i ≈ 6.9%

    Answer: i ≈ 6.9%

    32500 = 13000 · [1 + 0.07/2]^2t

    ln(32500/13000) = 2t ln(1.035)

    t = ln(2.5)/(2 ln(1.035))

    t ≈ 13.3 years

    Answer: ≈ 13.3 years

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