A deposit of $10,000 is made a year from now, a second deposit of $10,000 is made at the end of the year 5, and a deposit of $3000 is made at the end of year 8. The account earns 6% interest. You want to withdraw an equal amount, X at the end of each year for the next 10 years. What is the amount of X if the goal is to empty the account

$4068.77

Explanation:

We calculate the Future value of all the three deposits at the end of year 8

FV = CF1 *(1+r)^8-1 + CF5*(1+r)^8-5 + CF8 * (1+r)^8-8

FV = 10000 *(1+0.06)^7 + 10000*(1+0.06)^3 + 3000 * (1+0.06)^0

FV = 15,036.30 + 11,910.16 + 3,000

FV= $29,946.46

We have to calculate the annuity payments that have a Present value = $29,946.46

PV = PMT * 1-(1+r)^-n / r

PV = 29,946.46, PMT= ?, r = 6%, n = 10

29,946.46 = PMT * 1-(1+0.06)^-10 / 0.06

29,946.46 = PMT * 1 - 1.06^-10 / 0.06

29,946.46 = PMT * 1 - 0.558395 / 0.06

29,946.46 = PMT * 0.441605 / 0.06

29,946.46 = PMT * 7.36008

PMT = 29,946.46/7.36008

PMT = 4068.768274257889

PMT = $4068.77

Thus, amount of X is $4068.77 if the goal is to empty the account.

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