Andy needs to pay off a loan of $18,000 in 5 years. Find the amortization payment he would need to make each bi-monthly pay period (twice a month) at 6% compounded bi-monthly, in order to pay off
the loan.
To find the amortization payment, we can use the formula for calculating the monthly payment of a loan, and then adjust it for bi-monthly payments.
The formula for calculating the monthly payment of a loan is:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M is the monthly payment
P is the principal loan amount
r is the monthly interest rate
n is the number of months
First, we need to convert the bi-monthly interest rate to a monthly interest rate. Since there are 2 pay periods in a month, we divide the annual interest rate by 12 and then divide it by 2. In this case, the annual interest rate is 6%.
Monthly interest rate = (6% / 12) / 2 = 0.025
Next, we need to convert the loan duration to the number of months. Since there are 12 months in a year, we multiply the number of years by 12. In this case, the loan duration is 5 years.
Number of months = 5 * 12 = 60
Now, we can substitute the values into the formula to find the monthly payment:
M = 18000 * (0.025 * (1 + 0.025)^60) / ((1 + 0.025)^60 - 1)
Using a calculator, we can simplify this calculation to find the monthly payment Andy needs to make.
After finding the monthly payment, we can divide it by 2 to get the bi-monthly payment:
Bi-monthly payment = Monthly payment / 2
Finally, we can calculate the amortization payment that Andy would need to make each bi-monthly pay period to pay off the loan.