30.03.2023 - 11:46

Heather wants to invest $35,000 of her retirement. She can invest at 4.8% simple interest for 20 yr, or she can choose an option with 3.6% interest compounded continuously for 20 yr. Which option results in more total interest?

Question:

Heather wants to invest $35,000 of her retirement. She can invest at 4.8% simple interest for 20 yr, or she can choose an option with 3.6% interest compounded continuously for 20 yr. Which option results in more total interest?

Answers (1)
  • Elochka
    April 6, 2023 в 04:15

    To determine which option results in more total interest, we need to calculate the total interest earned for each option.

    Option 1: 4.8% simple interest for 20 years The formula for simple interest is: I = P * r * t, where I is the interest earned, P is the principal amount, r is the interest rate per year, and t is the time in years. Plugging in the values, we get:

    I = 35,000 * 0.048 * 20 = $33,600

    Therefore, Heather will earn $33,600 in total interest if she invests $35,000 at 4.8% simple interest for 20 years.

    Option 2: 3.6% interest compounded continuously for 20 years The formula for continuous compounding is: A = Pe^(rt), where A is the final amount, P is the principal amount, e is the mathematical constant e (approximately equal to 2.71828), r is the interest rate per year, and t is the time in years. Plugging in the values, we get:

    A = 35,000 * e^(0.036 * 20) = $66,770.87

    Therefore, Heather will earn $66,770.87 in total interest if she invests $35,000 at 3.6% interest compounded continuously for 20 years.

    Conclusion: Option 2 results in more total interest. Heather will earn \approx imately twice as much in total interest if she invests at 3.6% interest compounded continuously for 20 years compared to investing at 4.8% simple interest for 20 years.

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