I am trying to solve this problem from a Financial Mathematics exam:
John makes deposits of $450$ at the end of each quarter for $10$ years. At the end of $15$ years, he will use the fund to make annual payments of $Y$ at the beginning of each year for $4$ years, after which the fund is exhausted. Find $Y$ if $i = 7\%$ per annum.
The answer key indicates that the interest rate $r$ used to compute the future value of $450$ is given by $\left(1 + \dfrac{r}{m} \right)^{40} = 1.07$.
Why can’t I simply use $\dfrac{0.07}{4}$ as the interest rate? I cannot really wrap my head around which measurement of interest (nominal, effective, etc.) should be used.
