You will find in FM there are literally thousands of different ways to set up annuity problems and such. Do enough of them until you understand the basics and get to a point where you find whats most comfortable for you. Then its just a matter of repetition, for the most part.
Brandond, you want to change that. The first term should be (Original Loan Amount)(1+i)^3, which is the FV of the loan evaluated at time 3.
Your right, guess we were both wrong. I should have just accumulated the original loan amount, but the second part is correct. You just can't subtract out the payments, we need their future value at time 3 as well. Wouldn't you like to change yours as well?
Nah. In each level payment you make to amortize a loan, the interest is paid first, and the rest goes toward principal (lowering the total principal as long as your payment exceeds the interest payment). And assuming level loan payment, your principal repaid increases geometrically by a factor of (1+i).
This doesn't hold all the way through in this example, since the payment to amortize the loan is not level (it changes every 5 years). Nonetheless, each 5 year repayment period would show the principal repaid increasing by a factor of (1+i) [so P(5)=P(1)(1+i)^(5-1); P(10)=P(6)(1+i)^(10-6)].
Things get trickier when you pay a certain amount towards principal each year.