Question

please solve in word format instead of excel

Answer the question. $100,000 was deposited in a savings account 8 years ago, and the account earned interest at the rate of 10% per year. Assuming the end-of-the-year convention, what is the amount of equal annual withdrawals that can be made to completely deplete the fund 15 years from now if the first withdrawal will be made one year from today? I B Fi Initial Deposit $100,000,00 (P)

Answer 1

Amount Deposited 8 Years ago = X = $100000

Interest Rate = r = 10%

Number of Years = m = 8

Value of Investment now = PV = X(1+r)^m = 100000(1+0.10)⁸ = $214358.881

Let the amount withdrawn each year be P

Number of withdrawals = n = 15

Present Value of the amount = PV = $214358.881

Interest Rate = r = 10%

The present value of all the future withdrawals should be equal to the present value of the amount

=> PV = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r

=> 214358.881 = P[1- (1+0.10)^-15]/0.10

=> P = 214358.881*0.10/[1- (1+0.10)^-15] = $28182.57

Hence $28,182.57 can be withdrawn each year