Suppose you have recently purchased a house for which your mortgage
payment is $2000 for 30 years at 4%, what is the future value of your
payment?

Hi glen1234!!


Assuming monthly payments the formula for the future value of each payment is:
FV of PMT_i = (PMT_i) * (1 + Discount Rate/Period)^(Number of Periods -i)

If for example we consider a 5 periods payments (five payments) the
exponent (Number of Periods -i) causes the first payment to be
compounded 4 times into the future, the second payment to be
compounded 3 times into the future, etc.

The total Future Value is:
Future Value = Sum over all periods of the Future Value of Each payment =

If all payments are equal (this is the case of this problem), then:
FV = PMT/i * [(1 + i)^n - 1]

where:
FV = Future Value of the payments 
PMT = Amount of each payment 
i = Interest Rate Per Period 
n = Number of Periods 

For this problem is:
PMT = $2,000
i = 0.04 annual rate / 12 periods/year = 1/300
n = 30 years * 12 periods/year = 360 periods
then:
FV = $2,000/(1/300) * [(1+1/300)^360 - 1] =
   = $2,000 * 300 * [(301/300)^360 - 1] =
   = $600,000 * [(4/3)^360 - 1] =
   = $1,388,098.81

The future value of your payments is $1,388,098.81

NOTE: these cash flows at such rate correspond to a loan of
$418,922.48 . This result come from the use of the PV of payments
formula [1] on this problem, and can be easily checked by using the
future value formula for a single cash flow [2].
PV = PMT/i * [1 - (1 / (1 + i)^n]         [1]
FV = PV * (1 + i)^n                       [2]

See for references:
"Future Value of an Annuity":
http://www.getobjects.com/Components/Finance/TVM/fva.html

"Future Value Of A Single Amount":
http://www.getobjects.com/Components/Finance/TVM/fv.html

"Present Value of an Annuity":
http://www.getobjects.com/Components/Finance/TVM/pva.html

"Annuity Payments":
http://www.getobjects.com/Components/Finance/TVM/pmt.html



I hope that this helps you. Fell free to request for a clarificatoion
if you need it.

Regards.
livioflores-ga

---

Clarification of Answer by livioflores-ga on 17 Jul 2005 13:01 PDT

OooPs!!

Please let fix a typo at the FV calculation:

Please replace:
"FV = $2,000/(1/300) * [(1+1/300)^360 - 1] =
   = $2,000 * 300 * [(301/300)^360 - 1] =
   = $600,000 * [(4/3)^360 - 1] =   -------> Here is the typo
   = $1,388,098.81     "

by:
FV = $2,000/(1/300) * [(1+1/300)^360 - 1] =
   = $2,000 * 300 * [(301/300)^360 - 1] =
   = $600,000 * [(301/300)^360 - 1] =
   = $1,388,098.81

I forgot to replace a little mistake made during calculations (replace
4/3=1+1/3 by 301/300=1+1/300); but the result and resolution is good.

Thank you for your understanding,
Sincerely,
livioflores-ga