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?
Option B is the best choice, with a final balance $527,124.86.
Option A is the best choice, with a final balance of $362,175.91.
Option A is the best choice, with a final balance of $575,769.64.
Option B is the best choice, with a final balance of $342,936.58.
To determine which option is the best choice for Nouchi, we can calculate the final balances for both options after 25 years.
For Option A:
1. Calculate the monthly interest rate by dividing the annual interest rate by 12: 9% / 12 = 0.75% (or 0.0075 in decimal form).
2. Calculate the number of months in 25 years: 25 years * 12 months = 300 months.
3. Use the compound interest formula to calculate the final balance:
Final balance = Principal * (1 + monthly interest rate)^(number of months) + monthly contributions * (((1 + monthly interest rate)^(number of months) - 1) / monthly interest rate)
Final balance = $5000 * (1 + 0.0075)^(300) + $500 * (((1 + 0.0075)^(300) - 1) / 0.0075)
Final balance = $575,769.64
For Option B:
1. Calculate the monthly interest rate by dividing the annual interest rate by 12: 8% / 12 = 0.67% (or 0.00667 in decimal form).
2. Calculate the number of months in 25 years: 25 years * 12 months = 300 months.
3. Use the compound interest formula to calculate the final balance:
Final balance = Principal * (1 + monthly interest rate)^(number of months) + monthly contributions * (((1 + monthly interest rate)^(number of months) - 1) / monthly interest rate)
Final balance = $10,000 * (1 + 0.00667)^(300) + $300 * (((1 + 0.00667)^(300) - 1) / 0.00667)
Final balance = $527,124.86
Therefore, Option B is the best choice for Nouchi, with a final balance of $527,124.86.