Construct the amortization schedule for a 15,000 debt that is to be amortized in 10 equal semiannual payments at 6% interest per half-year on the unpaid balance
To construct the amortization schedule for a debt, you need to calculate the payment amount, interest payment, principal payment, and the remaining balance after each payment.
Let's break down the steps to create the amortization schedule for a $15,000 debt amortized in 10 equal semiannual payments at a 6% interest rate per half-year on the unpaid balance:
1. Calculate the payment amount:
To calculate the payment amount, you can use the formula for the present value of an annuity. The formula is:
PMT = PV * (r / (1 - (1 + r)^(-n)))
Where:
PMT = Payment amount
PV = Present value of the debt
r = Interest rate per period
n = Number of periods
In this case, the present value (PV) is $15,000, the interest rate (r) is 6% per half-year, and the number of periods (n) is 10.
Let's plug the values into the formula:
PMT = 15,000 * (0.06 / (1 - (1 + 0.06)^(-10)))
Now calculate the payment amount (PMT).
2. Calculate the interest payment:
For each payment, you need to calculate the interest payment based on the outstanding balance at the beginning of the period. The formula to calculate the interest payment is:
Interest Payment = Outstanding Balance * Interest Rate
3. Calculate the principal payment:
The principal payment is the difference between the payment amount and the interest payment. So, you can use the formula:
Principal Payment = Payment Amount - Interest Payment
4. Calculate the remaining balance:
The remaining balance is the outstanding debt after each payment. To calculate it, subtract the principal payment from the previous outstanding balance.
Now, using the formulas and calculations mentioned above, you can create the amortization schedule with 10 equal semiannual payments for the $15,000 debt at a 6% interest rate per half-year on the unpaid balance.