Question 4
Solution
Rate
7%
Compounded Annually
A tabulation shows this well.
Deposit
Withdrawal
Interest
Balance
0
$2,000.00
$0.00
$0.00
$2,000.00
1
$0.00
$0.00
$140.00
$2,140.00
2
$0.00
$0.00
$149.80
$2,289.80
3
$0.00
-$1,000.00
$160.29
$1,450.09
4
$0.00
$0.00
$101.51
$1,551.59
5
$3,000.00
$0.00
$108.61
$4,660.20
6
$0.00
$0.00
$326.21
$4,986.42
7
$0.00
$0.00
$349.05
$5,335.47
8
$1,500.00
$0.00
$373.48
$7,208.95
9
$0.00
$0.00
$504.63
$7,713.58
10
$0.00
$0.00
$539.95
$8,253.53
11
$0.00
$0.00
$577.75
$8,831.27
NPV
$5,011.97
($816.30)
$4,195.67
FW=
$8,831.27
Deposit
Withdrawal
Net
0
$2,000.00
$0.00
$2,000.00
1
$0.00
$0.00
$0.00
2
$0.00
$0.00
$0.00
3
$0.00
-$1,000.00
($1,000.00)
4
$0.00
$0.00
$0.00
5
$3,000.00
$0.00
$3,000.00
6
$0.00
$0.00
$0.00
7
$0.00
$0.00
$0.00
8
$1,500.00
$0.00
$1,500.00
9
$0.00
$0.00
$0.00
10
$0.00
$0.00
$0.00
11
$0.00
$0.00
$0.00
NPV=
$4,195.67
FW=
$8,831.27
Determine PV of each transaction, sum and determine future value.
Year
Amount
PV
Transaction
0
($2,000.00)
$2,000.00
3
$1,000.00
($816.30)
5
($3,000.00)
$2,138.96
8
($1,500.00)
$873.01
PW =
Sum
$4,195.67
11
FW
$8,831.27
Determine the FV in period 11 of each transaction, and sum.
Year
Amount
FV
Transaction
0
($2,000.00)
$4,209.70
3
$1,000.00
($1,718.19)
5
($3,000.00)
$4,502.19
8
($1,500.00)
$1,837.56
11
Sum = FW
$8,831.27
If you invest $2,000 today, withdraw $1,000 in 3 years, deposit $3,000 in 5 years, deposit
$1,500 in 8 years, and withdraw the entire sum 3 years after the final deposit, how much will
you withdraw? Interest is 7% compounded annually.
End of
year
An alternative is as follows.
Determine the PV of each deposit and each
withdrawal, sum these, and then find the future value in year 11 of this
sum.
Using negative signs that reflect the movement of money from
your pocket (deposits) and positive signs for what comes into your
pocket (withdrawals), makes the future value be positive, which it should
be.
Determine the NPV of deposits and withdrawals, sum, and
find future value in year 11.
The PV is entered as negative since the
tablulation had deposits as positive and
withdrawal as negative.
and find future value in year 11.
End of
year