The annual effective interest rate corresponds to the nominal rate of 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?
We can calculate the NPV for each deal
Deal A
Interest Rate = r = 10%
NPV = -CF0 + CF1/(1+r) + CF2/(1+r)2 + ..... = -4000 +
2000/(1+0.10) + 4000/(1+0.10)2 = 1123.97
Deal B
NPV = -CF0 - CF1/(1+r) + CF2/(1+r)2 + ..... = -2000 -
4000/(1+0.10) + X/(1+0.10)2 = -5636.36 +
X/1.102
Since both are equal,
=> 1123.97 = -5636.36 + X/1.102
=> X = (1123.97 + 5636.36)*1.102
=> X = $8180
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