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An ordinary annuity that earns 7.5% compounded monthly has a current balance of $500000. The owner of the account is about to retire

and has to decide how much to withdraw from the account each month.
Find the number of withdrawals under each of the following options:
(a) $5000 monthly (b) $4000 monthly (c) $3000 monthly

1 Answer

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We can use the formula for the present value of an ordinary annuity to find the number of withdrawals for each option:

PV = PMT x [1 - (1 + r/n)^(-nt)] / (r/n)

where PV is the present value (current balance), PMT is the withdrawal amount, r is the annual interest rate (7.5%), n is the number of times the interest is compounded per year (12 for monthly compounding), and t is the number of years.

(a) For PMT = $5000:
500000 = 5000 x [1 - (1 + 0.075/12)^(-12t)] / (0.075/12)
Simplifying and solving for t, we get:
t = 20.31 years
Therefore, the owner can withdraw $5000 per month for 20.31 years.

(b) For PMT = $4000:
500000 = 4000 x [1 - (1 + 0.075/12)^(-12t)] / (0.075/12)
Simplifying and solving for t, we get:
t = 24.85 years
Therefore, the owner can withdraw $4000 per month for 24.85 years.

(c) For PMT = $3000:
500000 = 3000 x [1 - (1 + 0.075/12)^(-12t)] / (0.075/12)
Simplifying and solving for t, we get:
t = 32.77 years
Therefore, the owner can withdraw $3000 per month for 32.77 years.

Note: These calculations assume that the interest rate and the monthly withdrawal amount remain constant over the entire period. In reality, the interest rate may fluctuate and the withdrawal amount may need to be adjusted over time to account for inflation and other factors.
User Dixit Singla
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