Calculate the yield rate on transaction

Question

Problem:-

'A' is able to borrow $1000 from 'B' for one year at 8% effective and at the same time lend it to 'C' for one year at 10% effective. what is 'A's yield rate on this transaction?

My answer:-

I calculated NPV by calculating the future values of 'A' in one year. considering FV(B) is negative (because he should pay it to 'B') and FV(C) is positive (because 'A' receives that amount from 'C' in one year). then I equated the NPV value to zero to find the Yield rate (IRR).

       - 1000(1.08)/(1+i) + 1000(1.1)/(1+i) = 0

then I get,

          20/(1+i) = 0

for this to be true, i must be equal to infinity.

is this the correct answer or did I made any mistakes there?

Answer 1

Your answer is correct, excellent work.

We could also write this as:

$$1000 (1.1) v - 1000 (1.08) v = 0 \rightarrow 20 v = 0 \rightarrow v = 0$$

So we have:

$$ v = \dfrac{1}{1 + i} = 0 \rightarrow i = \infty$$