Answer:
Yes there will be money left in the account after 10 years.
Step-by-step explanation:
The original amount at the start of retirement = $500,000
annual interest rate = 6% = 0.06
First of all, $4,000 is spent monthly for the next 10 years, let us calculate the total amount spent:
10 years of 12 months per year = 10 × 12 = 120 months
if $4,000 is spent per month, then total amount spent after 10 years (120 months) = 120 × 4000 = $480,000. This amount is less than the original saved amount of $500,000, hence, in the absence of any interest, the invested amount is higher than the amount spent by $20,000, suggesting that there will be some money left in the account after 10 years.
Next let us calculate the total amount on the sum if simple interest is applied on the original amount.
Simple interest = Principal × rate × time
Therefore simple interest on the sum for a period of 10 years =
500,000 × 0.06 × 10 = $300,000
hence the total return after 10 years =
500,000 + 300,000 = $800,000
Next, if $4,000 is spent monthly for the next 10 years, $480,000 will be spent in total (calculated above)
Therefore, amount left in the account = 800,000 - 480,000 = $320,000