Annuity Due formula

[mshmyob]

Alright all you math experts out there I need your help.

I have a formula for an annuity due calculation
fv = p * (((1 + i) ^ n - 1) / i) * (1 + i)

where
fv = future value
p = payments
i = interest rate
n = term

No problem there - everything is working as it should.

I now need a formula where the payements (p) change. They will change by a fixed percentage amount (ie: increase 3% a year for the term).

I need the formula ... any ideas?

cheers,

[r035198x]

Alright all you math experts out there I need your help.

I have a formula for an annuity due calculation
fv = p * (((1 + i) ^ n - 1) / i) * (1 + i)

where
fv = future value
p = payments
i = interest rate
n = term

No problem there - everything is working as it should.

I now need a formula where the payements (p) change. They will change by a fixed percentage amount (ie: increase 3% a year for the term).

I need the formula ... any ideas?

cheers,

A useful hint is that

p(i) = p(1+r)

where r is the percentage rate.

[mshmyob]

Are you sure you meant to put p (payments) on both sides of the equation? Because if you did then the equation is not equal as far as I can see.

Assuming payments is 200 and i is 3% and r is 2% the equation won't equal out.

cheers,

A useful hint is that

p(i) = p(1+r)

where r is the percentage rate.

[mshmyob]

Currently what I have done is put everything into a loop (if payments increase with inflation) and calculated the future value of each payment and added them. It is only a few lines of code and seems to work but I was wondering if there is a specific formula when payment are non-regular.

cheers,

[r035198x]

Alright all you math experts out there I need your help.

I have a formula for an annuity due calculation
fv = p * (((1 + i) ^ n - 1) / i) * (1 + i)

where
fv = future value
p = payments
i = interest rate
n = term

No problem there - everything is working as it should.

I now need a formula where the payements (p) change. They will change by a fixed percentage amount (ie: increase 3% a year for the term).

I need the formula ... any ideas?

cheers,

Perhaps I'm misunderstandin g your variables.
The formula I gave is for calculating the ith payment where the rate applied is a flat r% after for each payment.

[mshmyob]

Let me try to explain further. The formula I gave is for an Annuity Due (where payments are made at the start of a period as opposed at the end). Example if payments (p) are made monthly the payments are made on the 1st day as opposed to the last day. This formula assumes all payments are equal throughout the whole term (n).

In other words I save $200 (p) a month for 10 (n) years and get 8% (i) annually on my savings.

FV is how much the savings grows to.

That formula is a standard formula used in finance.

What I would like to do now is take into account where payments may increase in value.

Same as above where I save for 10 years and get 8% a year but now I start saving $200 a month for 1 year but the next year I increase my savings by say 3% (inflation). So in the 2nd year I am saving $206 a month for that year, in the 3rd year I save $206*1.03 = $212.18 etc. up to year 10.

The only way I can take into account the changes in payments is to calculate each year of payments seperately and sum them together. Easily done with the computer as I said a few lines of code in a loop but I was wondering if there is a formula to do the same. What I have done is known as "principal of additivity"


I hope that makes more sense. Thanks for your help so far.

cheers,

Perhaps I'm misunderstandin g your variables.
The formula I gave is for calculating the ith payment where the rate applied is a flat r% after for each payment.