Dr$.$ Zoidberg decided to buy a $2023$ Tesla Model S P$100$D Hatchback for $$130,000.$ After paying a down payment and taxes, Dr$.$ Zoidberg can finance the rest of the purchase price with a loan of $100,000$ for $5$ years at a promotional finance rate of $3\%$ APR compounded quarterly. Please answer the following questions:

a$.$ What is the effecting annual rate changed on this loan?

b$.$ What would be the quarterly payment on this loan?

c$.$ Dr$.$ Zoidberg also discovers that instead of the special promotional rate he can make an additional down payment of $$20,000$ that would lower his loan amount accordingly $($i$.$e$.$ by $$20,000).$ At what APR would Dr$.$ Zoidberg have the same quarterly payment with this option as with the initial promotional rate of $3\%?$

d$.$ Dr$.$ Zoidberg finds that he can get $1\mathrm{.}5\%$ APR if he elects option $($c$).$ What will his quarterly payment be under this option?

e$.$ Now assume that that payment frequenc

Looking only for the answer to E$.$ Given the question I kept the preceding ones for context. Thank you.