Finding the Optimal Rate for Equal Interest Earnings on Savings Accounts

[Imparcticle]

I have become completely bewildered by the following problem:
Suppose you are a bank manager determining rates on savings accounts. If the account with interest compounded annually offers 5% interest, what rate should be offered on an account with interest compounded daily in order for the interest earned on equal investments to be the same?
the annual investment, I'm guessing is $1000 because in part "a" of the question, it pointed the amount out, although for a slightly different situation. In part "a", it asked the reader to find the compounded interest for once, twice etc. times during the year.(there are 3 parts to it, btw and the one above is part "c").
The answer is 4.88%.
This is the formula I think you're supposed to use:

Compounded interest is defined by the following formula:
A=P(1+ r/n)^nt , where "A" is the total amount
"r" is the interest rate
"n" is number of times it's paid
"t" is the time
"P" is the principal

Just in case, I have typed up the rest of the problem:

a. How much interest would you earn in one year on an $1000 investment earning 5% interest if the interest is compounded once, twice, four times, twelve times, or 365 times in the year?
b.) If you are making an investment that you will leave in an account for one year which account shuld you choose to get the higheest return?
Account rate compounded
statement savings 5.1% yearly
money market savings 5.05% monthly
super saver 5% daily
c.)Suppose you are a bank manager determining rates on savings accounts. If the account with interest compounded annually offers 5% interest, what rate should be offered on an account with interest compounded daily in order for the interest earned on equal investments to be the same?
THE FOLLOWING ARE THE ANSWERS TO A,B,C:
Answers
A.) $50; $50.63; $50.94; $51.16; $51.26
B.) Money Market Savings
C.) 4.88%

Oh, and this is from a precalculus course I am enrolled in.

 

[Fermat]

Let r1 be the annual interest of 5%. This gives an annual "pay-out factor" of (1+r) on a principle of Po. i.e. over one year,

P = Po(1+r1)

Let r2 be the equivalent interest rate compounded daily. Then the "pay-out factor) is (1+r2/365)^365 on a principle of Po over a period of one year. i.e.

P = Po(1+ r2/365)^365

For the interest rates to be equivalent, the "pay-out factors" must be equal. i.e.

(1+r1) = (1+r2/365)^365

You know r1 is 5%, so you can solve for r2.