Question

You have sold your home and would like to travel the European country side. While you are out of the country, you would like the profit that you made on the sale of your home to gain interest while you are away in Europe. You made a profit of $25,000 on the sale of your home, and you invest this amount into an account paying 7.8% interest compounded annually. If you are to withdraw from the account over a 5 year period, such that by the end of the five year period there is zero dollars in the account, how much annually will you be able to withdraw from the account?

a.
$5,821.22
c.
$6,012.10
b.
$5,959.02
d.
$6,228.44

Answer 1

25000=X [((1-(1+0.078)^(-5))/0.078]
Solve for x
X=6228.44

Answer 2

D. $6228.44

Explanation:

We are given that,

Present value of the profit = $25,000

Rate of interest = 7.8% = 0.078

Time Period = 5

Now, we have the annuity formula
`P=(r * PV)/(1-(1+r)^(-n) )`, where P = annual withdrawn amount, PV = present value, r = rate of interest and n= time period.

So, substituting the given values gives,

`P=(0.078 * 25000)/(1-(1+0.078)^(-5) )`

i.e.
`P=(1950)/(1-(1.078)^(-5) )`

i.e.
`P=(1950)/(1-0.6869)`

i.e.
`P=(1950)/(0.3131)`

i.e.
`P=0.6228.042`

So, we get that the annual amount closest to the obtained P we can withdraw is $6,228.44.