You have the chance to buy a guaranteed promissory note for $$850.$ The note pays $$1,000$ in $15$ months $($i$.$e$.,$ exactly $456$ days$).$ You have $$850$ in a bank account that pays a $7\%$ nominal rate compounded daily. Which is a better investment, the note or the bank account? Answer this question using three approaches:

$(1)$

compare your future value if you buy the note versus leaving your money in the bank;

$(2)$

compare the PV of the note with your current bank balance; and

$(3)$

compare the effective rate or return on the note with that of the bank account.