Find the payment necessary to amortize a 8% loan of $1700 compounded quarterly, with 11 quarterly payments?
To find the payment necessary to amortize a loan, you can use the formula for the monthly payment of a loan:
PMT = (PV * r) / (1 - (1 + r)^(-n))
Where:
PMT = Payment amount
PV = Present value or loan amount
r = Interest rate per period
n = Total number of payment periods
In this case, we have a loan amount of $1700, an interest rate of 8% (0.08) compounded quarterly, and a total of 11 quarterly payments.
First, we need to convert the interest rate to a quarterly rate. Since the loan is compounded quarterly, we divide the annual interest rate by 4:
r = 8% / 4 = 2% or 0.02
Next, we substitute the values into the equation:
PMT = (1700 * 0.02) / (1 - (1 + 0.02)^(-11))
Simplifying further:
PMT = 34 / (1 - (1 + 0.02)^(-11))
To solve this equation, we can use a calculator or spreadsheet software to evaluate the expression inside the parentheses:
PMT = 34 / (1 - 0.81973)
PMT = 34 / 0.18027
PMT ≈ 188.42
Therefore, the payment necessary to amortize the loan is approximately $188.42.
x( 1 - 1.02^-11)/.02 = 1700
x( 9.786848.. = 1700
x = $ 173.70