Question

You are thinking about buying a piece of art that costs $20,000. The art dealer is proposing the following deal: He will lend you the money, and you will repay the loan by making the same payment every two years for the next 30 years. If the interest rate is 10% per year, how much will you have to pay every two years?

Answer 1

Solution:
	Payment every two years $4,455.33     or   $4,455.3 in one decimal
Working Notes:
	Payment every two years is called biennial payment
	Here the loan amount will be equal to Present value of annuity of biennial payment
	Interest rate given is annual but our payment is biennial means once in a two years so interest rate is also converted to biennial
	i=interest rate = (1+r)^2 - 1 =(1+ 0.10)^2 - 1   = 0.21 = 21%
	P= biennial payment = Payment every two years = ??
	n= no. Of payments= 30/2 = 15
	Present value of annuity of biennial payment = $20,000 the loan amount
	Present value of annuity = P x (1-(1/(1+i)^n))/i
	20,000 = P x (1-(1/(1+0.21)^15))/0.21
	20,000 = P x 4.489006889
	P = 20,000/4.489006889
	P = $4,455.328427
	P = $4,455.33
Please feel free to ask if anything about above solution in comment section of the question.