Suppose you accumulated $500,000, perhaps from many years of saving. You put the money in a savings plan earning 6% compounded monthly. If you want to live off the interest without disturbing the $500,000 balance, what amount can you withdraw at the beginning of each month?Group of answer choices$2,487.56$2,602.16$2,480.21$2,500.00
Question
Suppose you accumulated 500,000 balance, what amount can you withdraw at the beginning of each month?Group of answer choices2,602.162,500.00
Solution
To solve this problem, we need to use the formula for the monthly payout of an annuity, which is:
P = r(PV) / [1 - (1 + r)^-n]
where:
- P is the monthly payout
- r is the monthly interest rate
- PV is the present value of the annuity (the initial amount of money)
- n is the number of periods (months)
In this case, the annual interest rate is 6%, so the monthly interest rate r is 6% / 12 = 0.005 (or 0.5%).
The present value PV is $500,000.
We want to find the monthly payout P that will last indefinitely, so we can consider this as an annuity with an infinite number of periods. In this case, the formula simplifies to:
P = r(PV)
Substituting the given values:
P = 0.005 * 2,500.00
So, you can withdraw 500,000 balance.
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