Question

A 20 year loan of $50, 000 is taken out at effective annual interest i = 6% for the first 10 years and then i = 7% for the next 10 years. Payments are constant at the end of each year. Find the outstanding balance after the 16th payment.

Answer 1

Step-1:Calculation of annual payment
Annual payment	=	Loan amount	/	Cumulative discount factor
	=	$ 50,000.00	/	11.28202
	=	$   4,431.83
Working:
Present value of annuity of 1 for first 10 years	=	(1-(1+i)^-n)/i	Where,
	=	(1-(1+0.06)^-10)/0.06	i	=	6%
	=	7.36008705		n	=	10
Present value of annuity of 1 for next 10 years	=	((1-(1+i1)^-n)/i1)*(1+i2)^-n	Where,
	=	((1-(1+0.07)^-10)/0.07)*(1+0.06)^-10	i1	=	7%
	=	3.92193125		i2	=	6%
				n	=	10
Cumulative discount factor	=	7.36008705	+	3.921931
	=	11.2820183
Step-2:outstanding balance after the 16th payment
Outstanding Balance	=	Annual payment	*	Present Value of annuity of 1
	=	$   4,431.83	*	3.387211
	=	$ 15,011.55
Working:
Present value of annuity of 1 for first 10 years	=	(1-(1+i)^-n)/i	Where,
	=	(1-(1+0.07)^-4)/0.07	i	=	7%
	=	3.38721126		n	=	4