Question

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?

Answer 1

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