Question

Agus purchases a five year financial instrument having the following features : (a) Agus receives payments of $1,000 at the end of each year for five years. (b) These payments earn interest at an effective rate of 4% per annum. At the end of the year, this interest is REINVESTED at the effective rate of 5% per annum. Find the purchase price to Agus to produce a yield rate of 4% overall. Hint : Draw the time line diagram for payment series and interest series to make it easy. Calculate the total accumulated value in five years (future value in year 5th). The purchase price is the present value of total accumulated value (FV in year 5th) that yields 4% over these five years.

Answer 1

	Future Value of Cash Flow=(Cash Flow)*((1+i)^N)
	i=interest rate
	N=Number of years to future
	t	N=5-t	A	B	C=B*(1.05^N)
		Number of	Payment	Interest	Future
	Years From Today	Years to future	Received	at 4%	Value of interest
	1	4	$1,000
	2	3	$1,000	$40	$46.31
	3	2	$1,000	$80	$88.20
	4	1	$1,000	$120	$126.00
	5	0	$1,000	$160	$160.00
		Total	$5,000		$420.51
	Accumulated Value of Cash Flows=5000+420.51	$5,420.51
	Present Value of accumulated value	$4,455.26	(5420.51/(1.04^5))
	PURCHASE PRICE TO AGUS	$4,455.26