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?

• 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.