After looking at the results from questions 1, and 2. Seth realizes that a 2% return in a certificate of deposit will never allow him to reach his goal of $1 million in 10 years. Presuming his apartment will indeed be worth $400,000 in 10 years, compute the future value of Seth’s $100,000 investing using a 10%, 15%, and 20% return compounded semiannually for 10 years. Will any of these rates of return allow him to accomplish his goal of reach $1 million by age 55?

Question

After looking at the results from questions 1, and 2. Seth realizes that a 2% return in a certificate of deposit will never allow him to reach his goal of $1 million in 10 years. Presuming his apartment will indeed be worth $400,000 in 10 years, compute the future value of Seth’s $100,000 investing using a 10%, 15%, and 20% return compounded semiannually for 10 years. Will any of these rates of return allow him to accomplish his goal of reach $1 million by age 55?

Answer 1

P = Po(1+r)^n.

r = (10%/2)/100% = 0.05 = Semiannual % rate expressed as a decimal.

n = 2Comp./yr. * 10yrs = 20 Compounding periods.

P = 100,000(1.05)^20 = $265,329.77.

Repeat the above procedure for 15% and 20%.

Answer 2

To compute the future value of Seth's $100,000 investment, we can use the formula for compound interest:

Future Value = Principal * (1 + (Rate / n))^(n * time)

Where:
- Principal is the initial amount invested ($100,000)
- Rate is the annual interest rate (10%, 15%, or 20%)
- n is the number of times the interest is compounded per year (semiannually, meaning 2 times)
- time is the number of years (10 years)

Let's calculate the future values for each rate of return:

For a 10% rate of return compounded semiannually:
Future Value = $100,000 * (1 + (0.10 / 2))^(2 * 10) = $100,000 * (1.05)^20 = $100,000 * 2.6533 ≈ $265,330

For a 15% rate of return compounded semiannually:
Future Value = $100,000 * (1 + (0.15 / 2))^(2 * 10) = $100,000 * (1.075)^20 = $100,000 * 4.0462 ≈ $404,620

For a 20% rate of return compounded semiannually:
Future Value = $100,000 * (1 + (0.20 / 2))^(2 * 10) = $100,000 * (1.10)^20 = $100,000 * 6.1917 ≈ $619,170

Now, let's check whether any of these rates of return will allow Seth to reach $1 million by age 55:

As per the question, Seth's apartment will be worth $400,000 in 10 years. So, the total amount he needs to reach $1 million by age 55 would be $1,000,000 - $400,000 = $600,000.

Among the calculated future values, only the 20% rate of return yields a value that is greater than or equal to $600,000 ($619,170). Therefore, Seth will be able to accomplish his goal of reaching $1 million by age 55 if he invests his $100,000 with a 20% rate of return compounded semiannually for 10 years.