How do I use algebra to solve for a TVM/Annuity problem, calculating number of periods, when I am given the following: (1) starting sum (2) annual contributions (3) interest rate and (4) future value.

My corporate finance textbook does not indicate how this is accomplished without using a financial calculator.

Any assistance is greatly appreciated.

Don't know if it's too late for this...

You should not be given (1) and (4) together in the same problem if it's an annuity. You would have one of two situations:

You have a present value, like a loan or a retirement account you're going to pull payments out of, and then a set of payments that will reduce that amount. The "future value" would be zero because nothing would be left.

Or, you have a future value, like building up to retirement or a college fund or something like that, and you're making payments into it to build up to that amount. i.e. The "present value" is zero because you start with nothing.

But you can't mix a present and future together in the same equation when it's an annuity. (You can if it's not an annuity, but you're asking about annuities.)

These are the two equations:





Where i = interest per compounding period and n = number of compounding periods. (If these are all annual, then i is the annual rate and n is the years. If they aren't annual, you need to work by compounding periods, not years.)

Since you're using algebra, you can use these same equations to solve for payment -- you're just solving for a different "variable." You can also solve for n or i if you know the algebra to do it.