Question

Nouchi has two investment options. Option A offers 9% annual interest with a $5000.00 principal and contributions of $500 at the beginning of each month. Option B offers 8% annual interest with a $10,000.00 principal and contributions of $300 at the beginning of the month. If Nouchi plans to retire in 25 years, which option is the best choice for him?

a. Option A is the best choice, with a final balance of $575,769.64.
b. Option B is the best choice, with a final balance of $342,936.58.
c. Option B is the best choice, with a final balance $527,124.86.
d. Option A is the best choice, with a final balance of $362,175.91.

Answer 1

Option A is the best choice, with a final balance of $575,769.64.

Step-by-step explanation:

To determine which investment option is the best choice, we need to calculate the final balance of each option after 25 years. We can use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the final balance, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

For Option A, the principal is $5000, the annual interest rate is 9%, and contributions are made at the beginning of each month, which means interest is compounded monthly (n = 12).

So, A = 5000(1 + 0.09/12)^(12*25) = $575,769.64.

For Option B, the principal is $10,000, the annual interest rate is 8%, and contributions are made at the beginning of the month.

So, A = 10000(1 + 0.08/12)^(12*25) + 300((1 + 0.08/12)^(12*25) - 1)/(0.08/12) = $342,936.58.

Therefore, Option A is the best choice, with a final balance of $575,769.64.