Please note that in simple interest, the accumulated capital will be composed by the principal (P) plus the interests which are calculated as P*I*N, where I is the interest rate and N the amount of periods.

It the gives the formula P(N) = P(0)+P(0)*I*N, which is a linear function, similar to y=m*x+b (where y is P(N) and x is the time N - given that both P(0) and I are fixed values).

Hope this is clear. If not, please drop me a line and I'll get back to you.