Andy needs to pay off a loan of $18,000 in 5 years. Find the amortization payment he would need to take each semi-monthly pay period (twice a month) at 6% compounded bi-monthly, in order to pay off the loan.
To find the amortization payment Andy needs to take each semi-monthly pay period, we can use the formula for the amortization payment:
A = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
A = Amortization payment
P = Loan amount
r = Interest rate per period
n = Total number of periods
In this case, Andy's loan amount (P) is $18,000, the interest rate per period (r) is 6% compounded bi-monthly, and the total number of periods (n) is 5 years or 120 semi-monthly pay periods.
First, let's convert the annual interest rate to the bi-monthly interest rate:
Bi-monthly interest rate = (1 + annual interest rate)^(1/6) - 1
Bi-monthly interest rate = (1 + 6%)^(1/6) - 1
Bi-monthly interest rate = (1.06)^(1/6) - 1
Bi-monthly interest rate ≈ 0.009814
Using this bi-monthly interest rate, we can calculate the amortization payment using the formula:
A = $18,000 * 0.009814 * (1 + 0.009814)^120 / ((1 + 0.009814)^120 - 1)
After performing the calculations, the amortization payment (A) that Andy would need to take each semi-monthly pay period is approximately $290.17.
To calculate the amortization payment, we can use the formula for the monthly payment on a loan. However, since the loan is compounded semi-monthly (twice a month) and we are looking for a semi-monthly payment, we will need to adjust the interest rate and the number of periods accordingly.
First, let's convert the annual interest rate from 6% to a monthly interest rate by dividing it by 12 (number of months in a year):
Monthly Interest Rate = 6% / 12 = 0.06 / 12 = 0.005
Next, we need to adjust the number of periods. Since payments are made twice a month, the number of periods will be twice the number of years:
Number of Periods = 5 years * 2 = 10 semi-monthly periods
Now, we can use the formula for the monthly payment on a loan:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ (-Number of Periods))
However, since we are looking for a semi-monthly payment, we need to divide the monthly payment by 2:
Semi-Monthly Payment = Monthly Payment / 2
Now, let's substitute the values into the formula:
Semi-Monthly Payment = (18000 * 0.005) / (1 - (1 + 0.005) ^ (-10))
Calculating it using a scientific calculator or spreadsheet software, the semi-monthly payment is approximately $370.03.
Therefore, Andy would need to make a semi-monthly payment of $370.03 to pay off the loan over 5 years, with a 6% annual interest rate compounded bi-monthly.