Question

You take out a loan in the amount of $260,000 with annual equal repayments over the next 20years. What is the balance of the loan after the 5th payment? i = 6%

Answer 1

Step-1:Calculation of annual repayment
Annual repayment	=	Loan amount	/	Present value of annuity of 1
	=	$ 2,60,000.00	/	11.46992
	=	$     22,667.98
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.06)^-20)/0.06		i	6%
	=	11.46992122		n	20
Step-2:Calculation of loan balance after 5th payment
Loan amount is always present value of annual repayment discounted at interest rate.
So, loan balance after 5th payment	=	Present value of remaining 15 annual repayment
	=	Annual payment	*	Present value of annuity of 1
	=	$     22,667.98	*	9.712249
	=	$ 2,20,157.11
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.06)^-15)/0.06		i	6%
	=	9.712248988		n	15