Final answer:
To retire on a perpetuity that pays $3,000 per month with a retirement account paying 6% APR with monthly compounding, you would need a present value of $600,000.
Step-by-step explanation:
To calculate the present value required to retire on a perpetuity that pays $3,000 per month with a retirement account paying 6% APR with monthly compounding, we can use the formula for the present value of a perpetuity:
PV = C / r
Where PV is the present value, C is the cash flow per period, and r is the interest rate per period.
In this case, C = $3,000 per month and r = 6% APR / 12 months = 0.5% per month.
Plugging in the values, we get:
PV = $3,000 / 0.5% = $600,000
Therefore, the present value required to retire on a perpetuity that pays $3,000 per month is $600,000. So the correct answer is option a. $600,000.