Question

A property was purchased for ​$8036.00 down and payments of ​$1451.00 at the end of every six months for 4 years. Interest is 8 % per annum compounded annually. What was the purchase price of the​ property? How much is the cost of​ financing?

Answer 1

Semi annual rate is:

	Periodic interest rate=	(1+Effective annual interest rate)^ 1/m -1
r=	effective annual interest rate	8.0000%
m	number of periods	2
	Periodic interest rate=	(1+0.08)^1/2    -1
	Periodic interest rate=	3.9230%
	Nominal rate	7.84610%

a	Present value of annuity=	P* [ [1- (1+r)-n ]/r ]
P=	Periodic payment	1,451.00
r=	Rate of interest per period
	Annual interest	7.84610%
	Number of payments per year	2
	Interest rate per period	0.078460969082653/2=
	Interest rate per period	3.923%
n=	number of periods:
	Number of years	4
	Periods per year	2
	number of payments	8
	Present value of annuity=	1451* [ (1- (1+0.03923)^-8)/0.03923 ]
	Present value of annuity=	9,800.33
	Add: down payment	8,036.00
	Cost of property	17,836.33
	Total payments value	11,608.00
	Cost of financing	1,807.67