You have saved $26,704.00 for a three-year vacation to Germany. You will keep your money invested...

You have saved $26,704.00 for a three-year vacation to Germany. You will keep your money invested in an account paying 7.32% APR with monthly compounding while you live in Munich. You will make your withdrawals at the beginning of the month.

How much can you withdraw each month?

What is the balance on the account after the first month? (This is the balance prior to the withdrawal for the second month)

Expert Solution

Amount to be invest at the BEGINNING of each year = PV of Annuity = P*[1-{(1+i)^-n}]/i

Note: For the purpose of calculation (so that formula can be applied), it will be considered that amount will be received for 4 years at the end of each year starting from 1 year from now, and we will also add an additional annuity that will be received today. Effectively, we have a total of PV of next 4 installments and today’s installment.

Therefore, Present Value = PV of 35 Withdrawals + Today’s Withdrawal

Where, PV = $26704, i = Interest Rate = 0.073/12 = 0.006083, n = Number of Periods = (3*12)-1 = 35

Therefore,

26704 = P*[1-{(1+0.006083)^-35}]/0.006083 – P

26704 = P*31.43918 – P

26704 = 30.43918P

Therefore, Amount to be wtithdrawn each month = P = 26704/30.43918 = $877.29

Balance after 1st month = (Initial Balance-1st Withdrawal)*(1+Monthly Interest Rate) = (26704-877.29)*(1+0.006083) = 25826.71*1.006083 = $25983.82

jeff jeffy answered 2 years ago

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