7. Find the nominal interest rate that is equivalent to 18%/a, compounded quarterly, if interest is paid monthly.

To find the nominal interest rate that is equivalent to 18% per year, compounded quarterly, if interest is paid monthly, you can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A is the final amount after time t,
P is the principal amount,
r is the nominal interest rate,
n is the number of times interest is compounded per year, and
t is the time in years.

In this case, interest is compounded quarterly (n = 4), and since interest is paid monthly, the time period is also monthly, so t = 1 year / (12 months/year) = 1/12.

Let's assume the principal amount is $1.

Now we need to solve for the nominal interest rate, r.

Substituting the given values into the formula:

1 + r/4 = (1 + 0.18/12)^(12/4)
1 + r/4 = (1 + 0.015)^(3)
1 + r/4 = (1.015)^(3)
1 + r/4 = 1.045225
r/4 = 0.045225
r = 0.045225 * 4
r ≈ 0.1809

Therefore, the nominal interest rate that is equivalent to 18% per year, compounded quarterly, if interest is paid monthly, is approximately 18.09%.