Question

A business man borrowed P10000 with interest at the rate of 5% payable annually. The debt will be paid, principal and interest included, by equal payments at the end of each year for 5 years. Compute the annual payment and construct the amortization schedule.

Answer 1

ANNUAL PAYMENT: 2,309.75

AMORTIZATION SCHEDULE:

Year	Payment	Principal	Interest	Balance
0	-	-	-	10,000.00
1	2,309.75	1,809.75	500.00	8,190.25
2	2,309.75	1,900.24	409.51	6,290.01
3	2,309.75	1,995.25	314.50	4,294.76
4	2,309.75	2,095.01	214.74	2,199.75
5	2,309.75	2,199.76	109.99	(0.01)

*(0.01) is rounding difference.

• The loan is repaid in equal installments. Therefore, these installments are in the nature of an annuity.
• The present value of loan = 10,000 (i.e. present value of annuity)
• Present value of annuity = Annuity × PVAF (i%, n years)
  • i.e. Annuity = Present value of annuity ÷ PVAF (i%, n years)
  • ⇒ Annuity = 10,000 ÷ 4.32948 = 2,309.75
• This annual payment includes principal repayment and interest calculated on ending balance (of the previous year which is outstanding on the last day of the year; principal is repaid at the end of each year for 5 years).
  • E.g. Interest included in the first installment = 10,000 × 5% = 500
  • The remaining portion of the installment is principal repayment. Therefore, principal repayment included in the installment = annual installment - interest as calculated above. E.g. Principal repayment included in the first installment = 2,309.75 - 500 = 1,809.75
• Balance: It is the balance outstanding at the end of the year. Balance at the end of the year = Previous ending balance - principal repayment during the year.
• PVAF: Present value of annuity factor can be calculated using the following formula:
• 
  PV PVAF = 1 -(1+r)" Y =
  
  • r = interest rate
  • n = number of periods
    • PVAF_{(5%, 5 years)} = (1 - (1+0.05)^-5 )÷ 0.05 = 4.32948