There is 40,000 in a fund which is accumulating at 5% per annum convertible continuously.If money...

There is 40,000 in a fund which is accumulating at 5% per annum convertible continuously.If money is withdrawn continuously at the rate of 2,400 per annum, how long will the fund last?

Solutions

Expert Solution

We can find the answer using present value of annuity formula with continuous compounding.

Where,
PVA = Present value of annuity
A= Annuity (in our case it is the withdrawal amount)
e = mathematical constant (it has the value of 2.71828...)
r = rate of interest per annum
t = time in years

Substituting the known values, we get:

Now taking log on both sides, we get:

Therefore, it will last for 38.55 years.

Important note: for simplicity I have rounded off the calculations here so that I can cover maximum steps. But the final answer is correct, its intermediate calculations are not rounded off.

jeff jeffy answered 1 year ago

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