Question

What is the outstanding balance after the 23rd payment interval of a 23 year loan of $15,000 with semi-annual payments and an interest rate of 6% compounded semi-annually? Calculate answer to 2 decimal places.

Answer 1

	PV of annuity for making pthly payment
	P = PMT x (((1-(1 + r) ^- n)) / i)
	Where:
	P = the present value of an annuity stream	$      15,000
	PMT = the dollar amount of each annuity payment	To be computed
	r = the effective interest rate (also known as the discount rate)	6.09%	((1+6%/2)^2)-1)
	i=nominal Interest rate	6.00%
	n = the number of periods in which payments will be made	23
	15000=	PMT x (((1-(1 + r) ^- n)) / i)
	15000=	PMT * (((1-(1 + 6.09%) ^- 23)) / 6%)
	Annual payment=	15000/ (((1-(1 + 6.09%) ^- 23)) / 6%)
	Annual payment=	$   1,210.88
	Semi-annual payment=	$      605.44
	FV of 23rd payments=
	FV of annuity
	The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
	P = PMT x ((((1 + r) ^ n) - 1) / i)
	Where:
	P = the future value of an annuity stream	To be computed
	PMT = the dollar amount of each annuity payment	$   1,210.88
	r = the effective interest rate (also known as the discount rate)	6.09%
	i=nominal Interest rate	6.00%
	n = the number of periods in which payments will be made	11.5	23/2
	Future value of annuity payments=	PMT x ((((1 + r) ^ n) - 1) / i)
	Future value of annuity payments=	1210.88* ((((1 + 6.09%) ^ 11.5) - 1) / 6%)
	Future value of annuity payments=	$ 19,648.21
	FV of loan=	15000*(1+6%/2)^23
	FV of loan=	$ 29,603.80
	Remaining loan balance	29603.80-19648.21
	Remaining loan balance	$   9,955.59