Question

The annual effectiveinterest rate is 10% compounded monthly.

Deal A: You loan me $4000 today and I pay you back $2000 in 1 year, and $4000 in 2 years.

Deal B: I loan you $2000 today and another $4000 in 1 year and you pay me $X in 2 years.

What does $X have to be for you to be indifferent between these two deals?

Answer 1

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+10/(12*100))^12-1)*100

Effective Annual Rate% = 10.47

Deal A
Discount rate	0.1047
Year	0	1	2
Cash flow stream	-4000	2000	4000
Discounting factor	1	1.1047	1.220362
Discounted cash flows project	-4000	1810.446	3277.716
NPV = Sum of discounted cash flows
NPV Deal A =	1088.16
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Deal B
Discount rate	0.1047
Year	0	1
Cash flow stream	2000	4000
Discounting factor	1	1.1047
Discounted cash flows project	2000	3620.893
NPV = Sum of discounted cash flows
NPV Deal B =	5620.89
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

NPV B-NPV A = 5620.89-1088.16=4532.73

Future value = present value*(1+ rate)^time

Future value = 4532.73*(1+0.1047)^2

Future value = 5531.57