PMT FV Calculation

[mikethepenguin]

Hi all! I have always used the search function of this website to find solutions to my problems but for this one I cannot find the solution so I would require some help.
The problem is such (purely fictional )

Person X plans to retire at 60 and would like to take out £30,000 a year for 20 years thereafter. They have invested in a fund that returns 8%. Person X is 22 years old and plans to save until they are 50. How much should they save per year?
t = 50 - 22 = 28

Step 1 - I calculated the PV for year 60 which results = £331,532
Step 2 - I then calculated the PV which brings back that value to year 50 = £153,563
Step 3 - I calculate the PMT (for FV) and get = £1,610

My question is what is the formula behind PMT? I have tried most text book formulas and I haven't been able to get £1,610 (I kept getting £13,895)

I am using the function correctly, I just need to understand the principle behind it.

Any help will be appreciated!

 

[BarryL]

below is a description of PMT from the excel bible

PMT

The 
PMT function returns the loan payment (principal plus interest) per period, assuming constant

payment amounts and a fixed interest rate. The syntax for the 
PMT function is

PMT(rate,nper,pv,fv,type)

The following formula returns the monthly payment amount for a $5,000 loan with a 6 percent

annual percentage rate. The loan has a term of four years (48 months).

=PMT(6%/12,48,-5000)

This formula returns $117.43, the monthly payment for the loan. The first argument, 
rate, is the

annual rate divided by the number of months in a year. Also, notice that the third argument (
pv,

for present value) is negative and represents money owed.

 

[mikethepenguin]

below is a description of PMT from the excel bible

PMT

The 
PMT function returns the loan payment (principal plus interest) per period, assuming constant

payment amounts and a fixed interest rate. The syntax for the 
PMT function is

PMT(rate,nper,pv,fv,type)

The following formula returns the monthly payment amount for a $5,000 loan with a 6 percent

annual percentage rate. The loan has a term of four years (48 months).

=PMT(6%/12,48,-5000)

This formula returns $117.43, the monthly payment for the loan. The first argument, 
rate, is the

annual rate divided by the number of months in a year. Also, notice that the third argument (
pv,

for present value) is negative and represents money owed.

Thanks Barry but I am after the actual mathematic formula of the function. I can find the solution using PMT(rate,nper, ,fv) but I want to be able to do this calculation by hand.

 

[MickG]

Try :-
[TABLE="width: 519"]
<colgroup><col width="287" style="width: 215pt; mso-width-source: userset; mso-width-alt: 10211;"> <col width="100" style="width: 75pt; mso-width-source: userset; mso-width-alt: 3555;"> <col width="306" style="width: 229pt; mso-width-source: userset; mso-width-alt: 10865;"> <tbody>[TR]
[TD="class: xl63, width: 287, bgcolor: #DCE6F1"]Sum Req for 30K over 20Yrs @ 8% Annuity[/TD]
[TD="class: xl64, width: 100, bgcolor: #DCE6F1, align: right"]£294,544.42[/TD]
[TD="class: xl63, width: 306, bgcolor: #DCE6F1"]=(((1.08^20)-1)*30000)/((1.08^(20+1))-(1.08^20))[/TD]
[/TR]
[TR]
[TD="class: xl65, bgcolor: #D8E4BC"] [/TD]
[TD="class: xl65, bgcolor: #D8E4BC"] [/TD]
[TD="class: xl65, bgcolor: #D8E4BC"] [/TD]
[/TR]
[TR]
[TD="class: xl63, bgcolor: #DCE6F1"]Save per Yr, For 28 Yrs @ 8% for 294544.422[/TD]
[TD="class: xl64, bgcolor: #DCE6F1, align: right"]£2,860.60[/TD]
[TD="class: xl63, bgcolor: #DCE6F1"]=(294544.422*(1.08-1))/((1.08^(28+1))-1.08)[/TD]
[/TR]
</tbody>[/TABLE]