Question

Assume you have an adjustable rate mortgage with interest rates of 6% for year 1, 7% for year 2, 5% for year 3 and 4% for the remaining years of a 10 year mortgage. What is the rate of return if the original mortgage at time 0 is $700,000 and payments are made annually?

Answer 1

5.05%

Step-1:Calculation of cumulative discount factor
Discount factor of Year:
1	=	1.06^-1							=	0.943396
2	=	1.07^-1	*	1.06^-1					=	0.881679
3	=	1.05^-1	*	1.07^-1	*	1.06^-1			=	0.839694
4	=	1.04^-1	*	1.05^-1	*	1.07^-1	*	1.06^-1	=	0.807398
5	=	1.04^-2	*	1.05^-1	*	1.07^-1	*	1.06^-1	=	0.776344
6	=	1.04^-3	*	1.05^-1	*	1.07^-1	*	1.06^-1	=	0.746485
7	=	1.04^-4	*	1.05^-1	*	1.07^-1	*	1.06^-1	=	0.717774
8	=	1.04^-5	*	1.05^-1	*	1.07^-1	*	1.06^-1	=	0.690167
9	=	1.04^-6	*	1.05^-1	*	1.07^-1	*	1.06^-1	=	0.663622
10	=	1.04^-7	*	1.05^-1	*	1.07^-1	*	1.06^-1	=	0.638098
Total										7.704658
Step-2:Calculation of equivalent annual payment
Equivalent annual payment	=	Mortgage at time 0	/	Cumulative discount factor
		=	$ 7,00,000.00	/	7.704658
		=	$     90,854.13
Step-3:Calculation of rate of return
Rate of return	=rate(nper,pmt,pv,fv)
		= 5.05%
Where,
nper	=	10
pmt	=	$   -90,854.13
pv	=	$ 7,00,000.00
fv	=	0