Question

Roger is conducting a biochemical experiment for the next 12

months. In the first month, the expenses are estimated to be

$10,000. As the experiment progresses, the expenses are expected

to increase by

2 percent each month. Roger plans to pay for the

experiment with a government

grant, which is received in four

monthly installments, starting a month after the experiment

completion date. Draw the cash flow diagram for this experiment.

Determine the amount of the monthly installment so that the

installments received are equal in value to the expenses incurred.

Annual nominal interest is 1

0 percent, compounded monthly.

Answer 1

		Monthly Interest Rate=(10/12)%=	0.008333333
		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=Discount Rate=Monthly interest
		N=Month of Cash Flow
		Expense in Month1=	$10,000
		Expense in Month2=	$10,200	(10000*1.02)
		Expense in Month( N+1)=1.02*Expense in Month (N)
	N	Month	1	2	3	4	5	6	7	8	9	10	11	12
	A	Expense	$10,000	$10,200	$10,404	$10,612	$10,824	$11,041	$11,262	$11,487	$11,717	$11,951	$12,190	$12,434	SUM
	B=A/(1.008333333^N)	Present Value (PV) of Cash Flow:	$9,917	$10,032	$10,148	$10,266	$10,384	$10,505	$10,626	$10,749	$10,873	$10,999	$11,126	$11,255	$126,881
		Present value of expenses	$126,881
		Future Value at end of Month 12	$        140,167	(126881*(1.008333333^12)
	Nper	Number of Installment of grant	4
	Rate	Monthly interest rate	0.008333333
	Pv	Value of Grants at end of Month 12	$        140,167
	PMT	Monthly Grant Required	$35,775	(Using PMT function of excel with Rate=0.008333333,Nper=4, Pv=-140167)
		Excel Command :PMT(0.008333333,4,-140167)
		CASH FLOW DIAGRAM:
		Month	Cash Flow
		1	($10,000)
		2	($10,200)
		3	($10,404)
		4	($10,612)
		5	($10,824)
		6	($11,041)
		7	($11,262)
		8	($11,487)
		9	($11,717)
		10	($11,951)
		11	($12,190)
		12	($12,434)
		13	$35,775
		14	$35,775
		15	$35,775
		16	$35,775