Question

In 2009, Harold deposited $50,000 in an account paying 6% annual interest. Harold wants to make five equal annual withdrawals from the account starting with the first withdrawal in 2020. Further, Harold wants to have exactly $100,000 left in the account in 2026. How large can each of the annual withdrawals be

Answer 1

Answer:

Present value (PV) = 50,000

Future value (FV) = X

Rate of Interest (R) = 6%

No. of years (N) = 17

Balance Remain at the end of 17 years is 100,000

Thus, the Computation is as follows

FV = PV*((1+R/100)^N)/(1+R/100)  

FV= 50,000*((1+6/100)^17) / (1+6/100)

FV= 50,000*((1.06)^17) / 1.06

FV= 50000*2.7/1.06

FV= 135,000/1.06

FV = $127,358.49

Amount is required in the account = $ 100,000  

As, the total amount of 5 withdrawals ($127,358.49 - $100,000) = $27,358.49

The equal amount of Annual Withdrawal (Total Withdrawal / 5) = $5,468.82

Answer 2

Answer:

Yearly withdrawals: $ 5,796.954

Explanation:

Future value in 2020:

$Principal \: (1+ r)^{time} = Amount$

Principal 50,000.00

time 11.00

rate 0.06000

$50000 \: (1+ 0.06)^{11} = Amount$

Amount 94,914.93

Present Value of the 100,000 dollar in 2026 at 2020:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  $100,000.00

time  6.00

rate  0.06000

$\frac{100000}{(1 + 0.06)^{6} } = PV$  

PV   70,496.0540

Amount available for the withdrawals:

94,914.93 - 70,496.05 = 24.418,88‬

Annuity of 5 years that is possible with the available amount:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 24,418.88

time 5

rate 0.06

$24418.88 \div \frac{1-(1+0.06)^{-5} }{0.06} = C$

C  $ 5,796.954