Nine times a number is one more than ten times the number.

write an equation to find the number. then solve.

I will rewrite the wording and write out the equation as it goes so there is better understanding. Once I do that, I will solve it for you.
Nine times a number (9n) is (=) one more than ten times the number (10n + 1).
Now that we've rewritten it, let's only write what we have in parenthesis.
9n = 10n + 1.
Now that we have our equation, let's solve!
9n = 10n + 1
Subtract 10n from both sides.
-1n = 1
Divide both sides by -1.
n = -1
I hope this helps!

The interest rate would be 2.4%.

We start out finding the total amount he pays, including interest. 

78.40/month * 12 months * 5 years = $4704

We take off the amount of principal:
4704-4200 = 504

This is the amount of interest he pays.  Now we use the simple interest formula, I=prt:

504=4200(r)(5)

Multiply 4200 and 5:
504=21000r

Divide both sides by 21000:
504/21000 = 21000r/21000
0.024 = r
2.4% = r