Question

A firm borrows $5000 and the loan is to be repaid in 4 equal payments at the end of each of the next 4 years so that the ending balance at the end of year 4 is 0. The interest rate on the loan is 10 percent. The principal repayment in year 3 is:

Answer 1

Step-1:Calculation of annual payment
Annual payment	=	Loan amount	/	Present value of annuity of 1
	=	$       5,000	/	3.1698654
	=	$ 1,577.35
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.10)^-4)/0.10		i	10%
	=	3.1698654		n	4
Step-2:Calculation of loan amortization schedule
Year	Beginning balance	Interest Expense	Annual payment	Reduction in principal	Ending Balance
	a	b=a*10%	c	d=c-b	e=a-d
1	$ 5,000.00	$     500.00	$ 1,577.35	$ 1,077.35	$ 3,922.65
2	$ 3,922.65	$     392.26	$ 1,577.35	$ 1,185.09	$ 2,737.56
3	$ 2,737.56	$     273.76	$ 1,577.35	$ 1,303.60	$ 1,433.96
4	$ 1,433.96	$     143.40	$ 1,577.35	$ 1,433.96	$         0.00
The principal repayment in year 3 is $ 1,303.60