# Find the present value of the decreasing annuity necessary to fund the withdrawals. \$ 1530 per quarter for 25 years, if the annuity earns 6% per year. (Assume end of periodic deposits and compounding at the same intervals as deposits).

## Expert Answers To solve, apply the formula of present value of annuity.

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

where

PV is the present value

PMT is the periodic payment

r is the rate

n is the number of deposits/withdrawals in a year, and

t is the number of years.

Since \$1530 per quarter is to be withdrawn for 25 years, then PMT=1530, n=4 and t=25. And the given rate is s r=6%.

Plugging them to the formula yields:

`PV=(1530*[1-(1+0.06/4)^(-4*25)])/(0.06/4)`

`PV = (1530(1-1.015^(-100)))/0.015`

`PV = 78985.79661`

Rounding off to nearest hundredths, it becomes 78985.80.

Therefore, the present value is \$78985.80 .

Approved by eNotes Editorial Team

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