An elderly lady decided to distribute most of her considerable wealth to charity and keep for herself only enough money to provide for her living. She feels that $4500 a month will amply provide for her needs. She will establish a trust fund at a bank that pays 0.6% interest, compounded monthly. Upon her death, the balance is to be paid to her niece, Susan. If she deposits enough money to last forever, how much will Susan receive when her aunt dies?

To determine the amount of money the elderly lady needs to deposit in the trust fund, we need to use the concept of "compounded interest" and consider her monthly withdrawal of $4500.

The bank pays 0.6% interest compounded monthly, which means the interest rate per month is 0.6%/12 = 0.05%.

Let's denote the initial deposit as "P" and the interest rate per month as "r". Since the fund is supposed to last forever, the interest earned each month should be equal to the amount she withdraws ($4500).

We can express this as:
Interest = Withdrawal
P * r = $4500

Now, we can plug in the values for r:
P * 0.0005 = $4500

To find the initial deposit "P", we need to isolate it by dividing both sides of the equation by 0.0005:
P = $4500 / 0.0005
P = $9,000,000

So, the elderly lady needs to deposit $9,000,000 in the trust fund to ensure she can withdraw $4500 per month indefinitely.

When she passes away, her niece Susan will receive the balance, which will be the same as the initial deposit, since the interest earned is used for her monthly withdrawals.

Therefore, Susan will receive $9,000,000.

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