ippose you inherit a sum of money in an account worth $150,000. The account offe

Question

ippose you inherit a sum of money in an account worth $150,000. The account offers monthly. If you withdraw the money all at once, you will be pe- 3.2% annual interest compounded nalized heavily with taxes. Instead, you decide to withdraw a little bit each month. You will deposit other half you want the original account to be empty. You may ind the following formulas helpful: for various expenses and bills. You plan to do this for exactly ten years, at which point a) How much will you withdraw from the original account each month? 102.55 b.) How much will the new account be worth after the first has been emptied? e) How much interst has ben curied from both accoumt over these ten years? 239 S,j-156519,33

Explanation / Answer

we have 150000$ in the account

interest compounded monthly

monthly rate = 3.2/12*100 = 0.0027

we have the principle 150000 which will become 150000*1.0027 at the end of first month

we want to empty the amount in 10 yrs i.e. 120 months

suppose we withdraw x amount every month

and then put it at the same rate of 0.0027 per month for 120 months

at the ned of the 10 yrs period both will be same.

original amount 150000$ put for 120 months at the rate of 0.0027 per month

Total at the end of 120 months = 150000*1.0027120 = 206400 $

Now put x amount at the rate of r per month for n months

first x will earn interest for n months, second for n-1 months and last for 0 months

Total at the end of n-months = x + xr + xr3 + . . . . + x rn-1 + xrn  

= x( rn+1 -1)/(r-1)

here r = 1.0027 , n = 120 = x( 1.0027121 -1) /0.0027

=x 142.88

motnhly withdrawal x = 206400/142.88 = 1444.57$

b) half of this amount = 1444.57/2 = 722.29 $ is reinvested at 5.4% annual compounded monthly

monthly rate = 5.4/12*100 = 0.0045

r = 1+0.0045 = 1.0045

n = 120 months

total at the end of the period = 722.29 ( 1.0045121 -1) /0.0045

= 115830 $

c) From the first account

we got 1444.57 *120 over the period of 120 months

= 173348.4

priniciple = 150000

Interest earned = 23348.4 $

From second account Total accumulation = 115830 $

amout invested = 722.29*120 = 86674.8

interest earned = 29155.2

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