question 10 you want to be able to withdraw $25,000 from your account each year for 15 years after you…

question 10 you want to be able to withdraw $25,000 from your account each year for 15 years after you retire. you expect to retire in 30 years. if your account earns 10% interest, how much will you need to deposit each year until retirement to achieve your retirement goals? hint: you must first find the \required ending balance\ and then use that ending balance to calculate the \regular deposit amount\.

question 10 you want to be able to withdraw $25,000 from your account each year for 15 years after you retire. you expect to retire in 30 years. if your account earns 10% interest, how much will you need to deposit each year until retirement to achieve your retirement goals? hint: you must first find the \required ending balance\ and then use that ending balance to calculate the \regular deposit amount\.

Answer

Explanation:

Step1: Calculate the present - value of retirement withdrawals

We use the present - value of an ordinary annuity formula $PV = A\times\frac{1-(1 + r)^{-n}}{r}$, where $A=$25000$, $r = 0.1$, and $n = 15$. $PV=25000\times\frac{1-(1 + 0.1)^{-15}}{0.1}$ First, calculate $(1 + 0.1)^{-15}\approx0.239392$. Then $1-(1 + 0.1)^{-15}=1 - 0.239392 = 0.760608$. And $\frac{1-(1 + 0.1)^{-15}}{0.1}=\frac{0.760608}{0.1}=7.60608$. So $PV = 25000\times7.60608=$190152$. This is the required ending balance.

Step2: Calculate the annual deposit amount

We now use the future - value of an ordinary annuity formula $FVA=P\times\frac{(1 + r)^{n}-1}{r}$, where $FVA = 190152$, $r=0.1$, and $n = 30$. We need to solve for $P$. Rearranging the formula gives $P=\frac{FVA\times r}{(1 + r)^{n}-1}$. Calculate $(1 + 0.1)^{30}\approx17.4494$. Then $(1 + 0.1)^{30}-1=17.4494 - 1 = 16.4494$. And $\frac{r}{(1 + r)^{n}-1}=\frac{0.1}{16.4494}\approx0.00608$. So $P=\frac{190152\times0.1}{(1 + 0.1)^{30}-1}=\frac{19015.2}{16.4494}\approx$1156$.

Answer:

$1156$