Question

A payment of $16,000 is due in 1 year and $10,900 is due in 2 years. What two equal payments, one in 3 years and one in 4 years would replace these original payments? Assume that money earns 4.25% compounded quarterly.

Answer 1

$ 14,695.33

Step-1:Calculation of present value of cash flow
Quarter	Cash Flow	Discount factor	Present Value
a	b	c=1.010625^-a	d=b*c
4	$ 16,000	0.95860536	$ 15,337.69
8	$ 10,900	0.91892423	$ 10,016.27
Total			$ 25,353.96
Where,
Quarterly interest rate	=	4.25%/4
	=	0.010625
Step-2:Calculation of Two equal payment equivalent to above cash flow
Equal Payment	=	Present Value of cash flow	/	Cumulative discount factor
	=	$ 25,353.96	/	1.725307
	=	$ 14,695.33
Working:
Discount factor of :
3 Years	=	1.010625^-12	=	0.880886
4 Years	=	1.010625^-16	=	0.844422
Cumulative discount factor		1.725307