You would like to deposit a sum of money today that would enable you to withdraw $1, 000 a year for five years.If the interest paid on the amount deposited is 10% compounded annually and if the first withdrawal is made one year from today, the formula you would use to determine the amount of the initial deposit is
A)the present value of a deferred annuity
B)the present value of an annuity due
C)the present value of an ordinary annuity
D)the future value of an ordinary annuity

Question

Quizplus · Accepted Answer

The formula needed in this situation is the present value of an ordinary annuity, as the withdrawals are made at the end of each year. The formula for the present value of an ordinary annuity is:

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

where PV is the present value, PMT is the payment per period, r is the interest rate per period, and n is the number of periods.

In this case, PMT = $1,000, r = 0.10, n = 5, and we want to solve for PV:

PV = $1,000 * (1 - (1 + 0.10)^-5) / 0.10
PV = $3,791.55

Therefore, the initial deposit needed to generate the required withdrawals is $3,791.55.

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