I am going to give you $300,000 to invest, with the objective of growing it to $500,000

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Question:

I am going to "give you" $300,000 to invest, with the objective of growing it to $500,000 in 5 years so that you can take your $200,000 gain and use it as a down payment towards buying a house. However, the $300,000 is not "free" – you must pay me a fee, which I set equal to the yield-to-maturity on the 5-year Treasury scheduled to mature in 2028. That yield is now around 4.18%

Remember that the ytm on a bond is the average annual rate of return you can expect to earn over the life of the bond, if you hold it to maturity (and coupon reinvesting is done properly). Round all %'s to xx.yyy% or .xxyyy

a) Ignoring the fee for the moment, what is the monthly rate of return (compounded) that you must earn to achieve the portfolio objective if you contribute no additional money to the portfolio over the next 5 years?

b) Again ignoring the fee for the moment, what monthly rate of return must you earn on the portfolio if you can also save $325 per month towards the $500,000 objective?

c) How much $$$ is my fee, if the rate is applied (according to the definition of the ytm) to the initial $300,000 I "give" to you?

d) Now, including the amount of the fee that you will pay me from the portfolio's "liquidation proceeds" at the end of the 5th year (so that you pay me and still have $500,000 left over), what monthly rate of return must you earn on the portfolio if you can save $325 per month towards your new (revised with fee) objective?

e) Annualize the rate in (d).