Question

please help solve this problem

4. You and a friend are saving money for a summer in Europe after you graduate. You have each been depositing $500 each month into an interest bearing account so you can make 4 monthly withdrawals to pay for your trip. This investment account provides an annual interest rate of 5%, compounded monthly. a. Will you have saved enough money for the trip? b. If not, how much will you need to add to your last deposit (at the end of month 27)? If you do have enough, how much money will be left over at the end? Deposit, $ Withdrawal, $ Month 1-23 $500/month 24 $2800 $3100 $3100 $3100

Answer 1

4.

A.

Monthly interest rate R = 5%/12

PW of deposits = 500*(1-1/(1+5%/12)^23)/(5%/12)

PW of deposits = $10944.44

Now,

PW of the withdrawals = 2800/(1+5%/12)^24 + 3100*(1-1/(1+5%/12)^3)/(5%/12) * 1/(1+5%/12)^24

PW of the withdrawals = $10881.15

Since the PW of withdrawals is less than the PW of deposits, then enough money is saved.

----

B.

PW of the money left = 10944.44 - 10881.15 = $63.29

So,

Future value of excess money at the end of trip = 63.29*(1+5%/12)^27

Future value of excess money at the end of trip = $70.80 or $71