"Find the payment necessary to amortize a 4% loan of $2100 compounded quarterly with 13 quarterly payments. Find the payment size."

To find the payment necessary to amortize a loan, we can use the formula for the present value of an annuity:

P = (A * (1 - (1 + r)^-n))/r

Where:
P = Loan amount
A = Payment amount
r = Interest rate per period
n = Number of periods

In this case, the loan amount is $2100, the interest rate is 4% per year (or 1% per quarter), and there are 13 quarterly payments.

First, let's calculate the value of (1 + r)^-n:

(1 + r)^-n = (1 + 0.01)^-13

We can then substitute this value into the formula:

P = (A * (1 - (1 + r)^-n))/r

$2100 = (A * (1 - (1.01)^-13))/0.01

Solving this equation will give us the payment amount (A).

Let's calculate it.

P = ($2100 * (1 - (1.01)^-13))/0.01