Question

A student graduates with a total loan balance of​ $30,000 in a single loan with monthly payments for a term of 10 years at ​7% APR interest rate. What is the monthly payment for this​ loan? What will the unpaid balance be after 5​ years?

Answer 1

a.	Monthly payment	=	Loan amount	/	Present value of annuity of 1
		=	$ 30,000.00	/	86.12635
		=	$       348.33
	Working:
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.005833)^-120)/0.005833		i	=	7%/12	=	0.005833
		=	86.1263541		n	=	10*12	=	120
b.	Unpaid balance after 5 years	=	Monthly payment	*	Present value of annuity of 1
		=	$       348.33	*	50.50199
		=	$ 17,591.13
	Working:
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.005833)^-60)/0.005833		i	=	7%/12	=	0.005833
		=	50.5019935		n	=	5*12	=	60