Finding the Sum of a Geometric Series in Finance

Question

I have been stuck on these two problems forever, I have tried using the Sum of a Finite Geometric Series formula, but I cannot get to the intended final product of 200(1.005^(n)-1). I even double checked to make sure the -1 did not have to be in the exponent, I am just at wits end! For clarification, I need help with solving Questions 5 and 6. Mathematics of Loans Q5 and Q6

Answer 1

Note that's only the part in paretheses from (4), not the full answer.

Are you using $1 + r + r^2 + \cdots + r^k = \dfrac{r^{k+1}-1}{r-1}$ ?

In this case, $r=1.005$, so $\dfrac1{r-1} = \dfrac1{0.005} = 200$.

You would also use $k=n-1$, so $r^{k+1}-1 = r^n - 1$.

Putting it together, you do indeed get the answer they suggest.