Post a New Question

PreCalc

posted by .

Find the amount of time required to double a dollar investment at 7.72%, if the interest is compounded continuously.

4.49 years
8.98 years
17.96 years

I'm not understanding this, I got 3.9 years when I tried to solve this.

  • PreCalc -

    The basic formula for compounding continuously is:
    Lim (1+r/n)^(nt)
    as n→∞
    where t=number of years, and r is the annual interest rate.
    which results in the formula:
    A(t)=A(0)e^(rt)
    For doubling,
    A(t)/A(0)=2
    Therefore:
    e^(0.0772t) = 2

    Take natural log on both sides to get:
    0.0772t = ln(2)
    Solve for t.

  • PreCalc -

    continuous compounding formula is

    amount = principal(e^(it)) , so

    2 = 1(e^.0772t)
    ln2 = ln (e^.0772t)
    .0772 lne = ln2 , but ln e = 1
    t = ln2/.0772 = 8.98

    how did you get 3.9 ?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. compound interest

    How do I solve these problems? Complete the table for a savings account in which interest is compounded continuously. 1. Initial Investment: $1000 Annual % Rate: 3.5% Time to Double: ?
  2. algebra- Help fast

    use the compound interest formula A=P(1+r/n)^nt and A=Pe^rt to solve 1-Find the accumulated value of an investment of $5000 at 9% compounded continuously for 6 years. 2-Find for an investment of $700 at 16% compounded quarterly for …
  3. Math

    If 3000 dollars is invested in a bank account at an interest rate of 6 per cent per year, find the amount in the bank after 12 years if interest is compounded annually Find the amount in the bank after 12 years if interest is compounded …
  4. Calculus :)

    If 8000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the amount in the bank after 11 years if interest is compounded annually ____ Find the amount in the bank after 11 years if interest is …
  5. Compound interest

    Hello My teacher skipped over this and I have no clue how to do this or the equations. Help would be wonderful thank you If 6000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the amount in …
  6. algebra

    Hannah invests $3850 dollars at an annual rate of 6% compounded continuously, according to the formula A=Pe^rt, where A is the amount, P is the principal, e=2.718, r is the rate of interest, and t is the time, in years. (a) Determine, …
  7. math

    If $3500 is invested at an interest rate of 6.25% per year, compounded continuously, find the value of the investment after the given number of years. a) 3 years b) 6 years c) 9 years
  8. Calculus Please help!

    If 7000 dollars is invested in a bank account at an interest rate of 7 per cent per year. A) Find the amount in the bank after 6 years if interest is compounded annually?
  9. Pre-calculus

    Complete the table assuming continuously compounded interest. (Round your answers to two decimal places.) Initial Investment: Annual % Rate: Time to Double: 8 yr Amount After 10 Years: $1700 I don't understand how to get in the initial …
  10. Math

    Thor invests some money in an account earning 8% interest, compounded continuously. After how many years will he double his investment?

More Similar Questions

Post a New Question