approximately how much must be saved for retirement in order to withdraw $100,000 per year for the next 25…

approximately how much must be saved for retirement in order to withdraw $100,000 per year for the next 25 years if the balance earns 8% annually, and the first payment occurs 1 year from now? (round to the nearest thousand dollar.) a $1,067,000 b $1,250,000 c $2,315,000 d $2,500,000 e none of these are correct

approximately how much must be saved for retirement in order to withdraw $100,000 per year for the next 25 years if the balance earns 8% annually, and the first payment occurs 1 year from now? (round to the nearest thousand dollar.) a $1,067,000 b $1,250,000 c $2,315,000 d $2,500,000 e none of these are correct

Answer

Explanation:

Step1: Identify the present - value of an ordinary annuity formula

The formula for the present - value of an ordinary annuity is $PV = A\times\frac{1-(1 + r)^{-n}}{r}$, where $PV$ is the present value (the amount to be saved now), $A$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of periods.

Step2: Determine the values of $A$, $r$, and $n$

We have $A=$100000$, $r = 0.08$ (8% annual interest rate), and $n = 25$ years.

Step3: Substitute the values into the formula

[ \begin{align*} PV&=100000\times\frac{1-(1 + 0.08)^{-25}}{0.08}\ &=100000\times\frac{1 - 0.1460177}{0.08}\ &=100000\times\frac{0.8539823}{0.08}\ &=100000\times10.674776\ &= 1067477.6 \end{align*} ] Rounding to the nearest thousand dollars, $PV\approx$1067000$.

Answer:

A. $1,067,000