"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