(Complex present value) You would like to have $57,000 in 16 years. To accumulat
ID: 2615738 • Letter: #
Question
(Complex present value) You would like to have $57,000 in 16 years. To accumulate this amount you plan to deposit each year an equal sum in the bank, which will earn 5 percent interest compounded annually. Your first payment will be made at the end of the year a. How much must you deposit annually to accumulate this amount? b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum deposit be? (Assume you can earn 5 percent on this deposit.) c. At the end of 5 years you will receive $10,000 and deposit this in the bank toward your goal of S57,000 at the end of 16 years. In addition to this deposit, how much must you deposit in equal annual deposits to reach your goal? (Again assume you can earn 5 percent on this deposit.)Explanation / Answer
We will use financial calculator BA II Plus to solve, please enter the details in your calculator as per table:
I/Y = Rate; FV = Future value; PV = Present value; N = Number of terms; PMT = Payments
-----------------------------------------
a.
Annual payment should be $2,409.38 to achieve target of $57,000
I/Y =
5
FV =
-$57,000
N =
16
PV =
0
CPT > PMT =
$2,409.38
b.
Today we should deposit $26,112.36 to achieve $57,000
I/Y =
5
FV =
-$57,000
N =
16
PMT =
0
CPT > PV =
$26,112.36
c.
We have to break this problem in 2 parts; 1) We should calculate the FV of $10,000 for 11 years because we are going to receive this sum after 5 years and hence it will stay for 11 years only.
2) After getting FV of $10,000 we should subtract the amount from the target FV of $57,000
I/Y =
5
PV =
-$10,000
N =
11
PMT =
0
CPT > FV =
$17,103.39
Now, required additional future value is $57,000 - $17,103.39 = $39,897.61
I/Y =
5
FV =
-$39,897.61
N =
16
PV =
0
CPT > PMT =
$1,686.43
Hence, we are required to deposit only $1,686.43 annually considering the $10000 coming in end of 5th year and which will be invested for 11 years.
I/Y =
5
FV =
-$57,000
N =
16
PV =
0
CPT > PMT =
$2,409.38
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