You are deciding whether to purchase an annual pass or two, semester parking permits. Annual permits cost $$410.$ Semester permits cost $$163$ due on August $15$th and January $15$th$.$ Assuming monthly compounding, what is the rate of return for the annual permit?

You Answered

Correct Answer

$36\mathrm{.}9$ margin of error $\frac{+}{-}3$

To find the rate of return we must compare the cost of the annual permit versus $2,$ semester permits, where:

$PW$ an $=$ annual permit cost, and $P{W}_{\text{s}\text{e}\text{m}}=$ semester permit cost

To find the rate of return we set the two equal such that:

$P{W}_{an}=P{W}_{\text{s}\text{e}\text{m}}+P{W}_{\text{s}\text{e}\text{m}}(\frac{P}{F},i\%,5)$

This means we buy either one annual permit or buy one semester permit, then wait $5$ months $($August to January$)$ to buy the second one.

$i=$ RoRmonthly

$i_a=(1+i{)}^{12}$

$Ro{R}_a={100}^{**}{i}_a$ How can i get the correct answer?