Question

a desirable lot has become availble to jenkins company at a purchase price of 800000. jenkins is able to make a 10% down payment and then will mke annual payments at the beginnign of each of the next 25 years at an interest rate of 6%. what should jenkins expect the annual payment to be

Answer 1

Solution:
	Annual payment	$53,135.13
Working Notes:
	Purchase Price = 800,000
	Down payment = 10% = 10% of purchase price = 10% x 800,000 = 80,000
	Loan amount = Purchase price - Down payment
	Loan amount =800,000 - 80,000=720,000
Since,	Annual payments are made at beginning of year, the payments are of nature of annuity due.
	Loan amount is the present value of annuity due of annual payments for 25 years
	Present value of the annuity due at t=0 = P x [1-(1/(1+i)^n)] (1+i) / i
	Present value of the annuity due = Loan amount = $720,000
	P= Annual payments =??
	i=interest rate = 6%=0.06
	n= no. Of years= 25 Year
	Present value of the annuity at t=0 = P x (1-(1/(1+i)^n))(1+i) / i
	$720,000 = Annual payments x (1-(1/(1.06)^25))(1+0.06)/0.06)
	$720,000 = Annual payments x 13.55035753
	Annual payments = $720,000/13.55035753
	Annual payments = $53,135.12934
	Annual payments = $53,135.13
Please feel free to ask if anything about above solution in comment section of the question.