Construct a schedule for the amortization of:
(a) a debt of $15,000,000 with interest at 12% by 5 equal annual payments.
(b) a debt of $25,000,000 with interest at 12.5% compounded semi-annually by making 6 equal semi-annual payments.
a)
First we have to find the payment, assume it is made at the end of each year
15000000= pay( 1 - 1.12^-5)/.12
pay = 4161145.98
Paym# interest principal Balance
1 1800000.00 2361145.98 12638854.02
2 1516662.48 2644483.45 9994370.52
3 1199324.46 2961821.52 7032549.01
4 843905.89 3317240.10 3715308.91
5 445837.07 3715308.91 0.00
not bad,
now do b) the same way
your payment equation will be
25000000 = pay( 1 - 1.0625^-6)/.0625
To construct a schedule for the amortization of a debt, we need to calculate the payment amount and distribute it over the specified period. Let's calculate the payment amount and then create the amortization schedules for both scenarios.
(a) Debt of $15,000,000 with interest at 12% by 5 equal annual payments:
1. Calculate the annual interest rate, which is equivalent to the 12% stated, divided by 100: 12% / 100 = 0.12.
2. Determine the payment amount by dividing the total debt by the number of payments: $15,000,000 / 5 = $3,000,000 per year.
3. Prepare the amortization schedule as follows:
Year 1:
- Beginning Balance: $15,000,000
- Interest Expense: $15,000,000 * 0.12 = $1,800,000
- Principal Payment: $3,000,000 - $1,800,000 = $1,200,000
- Ending Balance: $15,000,000 - $1,200,000 = $13,800,000
Year 2:
- Beginning Balance: $13,800,000
- Interest Expense: $13,800,000 * 0.12 = $1,656,000
- Principal Payment: $3,000,000 - $1,656,000 = $1,344,000
- Ending Balance: $13,800,000 - $1,344,000 = $12,456,000
Continue this process for Year 3, Year 4, and Year 5 until the debt is fully amortized.
(b) Debt of $25,000,000 with interest at 12.5% compounded semi-annually by making 6 equal semi-annual payments:
1. Calculate the semi-annual interest rate, which is equivalent to the 12.5% stated, divided by 100: 12.5% / 100 = 0.125.
2. Determine the semi-annual compounding period, which is twice a year.
3. Determine the semi-annual interest rate by dividing the annual interest rate by the compounding periods: 0.125 / 2 = 0.0625.
4. Calculate the payment amount using the formula for calculating loan payments:
Payment Amount = Principal / Present Value Annuity Factor
Enlisting the help of a financial calculator or spreadsheet software, we can input the values to obtain the payment amount.
5. Prepare the amortization schedule as follows:
Semi-Annual Period 1:
- Beginning Balance: $25,000,000
- Interest Expense: $25,000,000 * 0.0625 = $1,562,500
- Principal Payment: Payment Amount - Interest Expense
- Ending Balance: Beginning Balance - Principal Payment
Continue this process for Semi-Annual Period 2, 3, 4, 5, and 6 until the debt is fully amortized.
Note: The calculation of the payment amount requires additional information, such as the compounding period and time period, which were not provided in the question.