Find the payment necessary to amortize a 4% loan of $2100 compounded quarterly with 13 quarterly payments. Find the payment amount.
quarterly rate = i = .04/4 = .01
Pay( 1 - 1.01^-13)/.01) = 2100
12.13374 (pay) = 2100
pay = $173.07
To find the payment necessary to amortize a loan, we can use the Amortization Formula:
P = r(PV) / (1 - (1 + r)^(-n))
Where:
P = Payment amount
r = Interest rate per period (compounded quarterly)
PV = Present value of the loan
n = Number of periods (in this case, the number of quarterly payments)
In this case, the loan amount (PV) is $2100, the interest rate (r) is 4% (or 0.04), and the number of periods (n) is 13.
Let's plug in the values and calculate the payment amount.
P = 0.04 * 2100 / (1 - (1 + 0.04)^(-13))
Now, let's evaluate the expression.
P = 0.04 * 2100 / (1 - (1.04)^(-13))
Calculating the result further:
P = 0.04 * 2100 / (1 - 0.443729)
P = 84 / 0.556271
Finally, we can find the payment amount:
P ≈ $151.08
Therefore, the payment necessary to amortize a 4% loan of $2100 compounded quarterly with 13 quarterly payments is approximately $151.08.