What is the present value of a trust fund that earns 9% compounded monthly and pays out $950 every month? The next payment will be made today.

Question

Quizplus · Accepted Answer

We can use the formula for present value of an annuity:

PV = PMT * ((1 - (1 + r/n)^(-nt)) / (r/n))

PV = $950 * ((1 - (1 + 0.09/12)^(-12*infinity)) / (0.09/12)) 
(Note: Since the payments continue indefinitely, we use "infinity" as the number of periods.)

PV = $950 * ((1 - 0) / 0.0075)

PV = $126,666.67

However, since the question asks for the present value at the time of the first payment (today), we need to discount the answer by one month's worth of interest.

PV = $126,666.67 / (1 + 0.09/12)

PV = $127,616.73

Therefore, the correct answer is D.

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