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Question: A person has $100,000 in a saving account that earns interest of 5% per year, compounded annually...

A person has $100,000 in a saving account that earns interest of 5% per year, compounded annually. If the person withdraws $5,000 at the end of each year, after how many years (a whole number) will the saving be exhausted? Will it ever get exhausted? can you please do this without the financial calculator

Answer 1

The total savings represent the present value of future withdrawals.

PV of annuity = P*[(1-(1+r)^(-n)) / r]

P - Periodic withdrawal = 5000

r - rate per period = 5%

n - number of periods = ?

100000 = 5000*((1-(1+0.05)^(-n)) / 0.05)

20*0.05 = 1-1.05^(-n)

1 = 1 - 1.05^(-n)

1.05^-n = 0

n is infinity. In other words, the interest earned on the principal each year will be 100000*0.05 = 5000, which is same as the amount withdrawn. So the principal remains intact. So, the savings will never get exhausted.