Ask Question
6 February, 04:27

Johan invests $4,000 at age 22 from the signing bonus of his new job. He hopes the investment will be worth $240,000 when he turns 66. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.

+1
Answers (2)
  1. 6 February, 06:41
    0
    The interest rate needs to be 9.8% for the sum of $4000 to compound to $240,000

    Step-by-step explanation:

    Since the interest compounds itself, hence the question concerns the compound interest.

    Details provided-

    Principal (Initial contribution) - $ 4000

    Amount (Expected amount) - $ 240,000

    Time period - investment started at 22 years and would continue until 66 years.

    Time period = 66-22 years = 44 years

    Rate of interest=

    We know that for compound interest-

    ⇒Amount = principal (1+rate/100) ⁿ

    Substituting the values if Amount, principal and time ("n") in the above equation

    240,000 = 4000 (1+rate/100) ⁴⁴

    240,000/4000 = (1+rate/100) ⁴⁴

    Solving the above equation would yield us with the rate as 9.75% ≈ 9.8% (rounded off to tenth place after decimal)

    Hence the Interest rate required by John would be 9.8%
  2. 6 February, 07:59
    0
    Answer: 9.3%

    Step-by-step explanation:

    Identify the variables of the formula:

    A = $240,000

    P = $4,000

    r=?

    t = 44 years (66-22=44)

    A = Pe^rt

    Substitute the values into the formula

    240,000 = 4,000e^r•44

    Solve for r. Divide each side by 4,000

    60 = e^44r

    Take the natural log of each side

    ln60 = ln e^44r

    Use the power property and then simplify

    ln60 = 44r ln e

    ln60 = 44r

    Divide each side by 44

    ln60/44=r

    Approximate the answer

    r = 0.09305 - -> r = 9.3%
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Johan invests $4,000 at age 22 from the signing bonus of his new job. He hopes the investment will be worth $240,000 when he turns 66. If ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers