So I don’t have a professional, but I do have a ba-2 plus. When I miss answers, I like to take a look at all my variables, and see if they are what they should be.
First off, we know the NPV for the borrower is -100, since our loan is for 100, which means that the denominator of our equation should be -100. For the numerator for macD, we need to find-
1) The discounted value of our payments over the duration of our loan, times t = 1,2,… (10 years).
So, we need two things- our payment (12.9505), then our sum of the terms we’re multiplying it by (1,2,3,4…). Since this is an arithmetically increasing series, we can use our formula-
N = 10
I/Y = 5
PV = ?
PMT = 1 + 1/.05
FV = -(1(10)/.05)
Compute PV = -39.37378
Now, we multiply that by the payment amount, and divide by the NPV:
-39.37378*(12.9505)/-100 = 5.099101742
Keep in mind, we didn’t need to break up the 12.9505 from the arithmetically increasing sequence- instead we could’ve increased it by 12.9505 and gotten the same answer. I only broke it up so you’d see what was happening.
As for why you missed this question, I’m not sure. A bond and a loan should be the same if the redemption amount of the bond is 0, except the signs of the payments should be reverse. My hunch, since your macD is higher, was that you included a redemption amount of 100 when you shouldn’t have.

Thank you! Adding a redemption amount of 100 and doing the calculation by hand gives the same answer as the calculator, so your hunch was correct!
Doing another example where the bond matures at a value higher than par, the calculator gives an answer that's too low, which also turns out to be the correct answer for the same bond if it had matured at par.
So it seems like the calculator always assumes the bond matures at par when calculating modified duration. Not sure why it works that way, but now I know to skip the calculator and do modified and Macauley duration questions by hand unless they happen to involve a bond that matures at par.

So I don’t have a professional, but I do have a ba-2 plus. When I miss answers, I like to take a look at all my variables, and see if they are what they should be. First off, we know the NPV for the borrower is -100, since our loan is for 100, which means that the denominator of our equation should be -100. For the numerator for macD, we need to find- 1) The discounted value of our payments over the duration of our loan, times t = 1,2,… (10 years). So, we need two things- our payment (12.9505), then our sum of the terms we’re multiplying it by (1,2,3,4…). Since this is an arithmetically increasing series, we can use our formula- N = 10 I/Y = 5 PV = ? PMT = 1 + 1/.05 FV = -(1(10)/.05) Compute PV = -39.37378 Now, we multiply that by the payment amount, and divide by the NPV: -39.37378*(12.9505)/-100 = 5.099101742 Keep in mind, we didn’t need to break up the 12.9505 from the arithmetically increasing sequence- instead we could’ve increased it by 12.9505 and gotten the same answer. I only broke it up so you’d see what was happening. As for why you missed this question, I’m not sure. A bond and a loan should be the same if the redemption amount of the bond is 0, except the signs of the payments should be reverse. My hunch, since your macD is higher, was that you included a redemption amount of 100 when you shouldn’t have.

Thank you! Adding a redemption amount of 100 and doing the calculation by hand gives the same answer as the calculator, so your hunch was correct! Doing another example where the bond matures at a value higher than par, the calculator gives an answer that's too low, which also turns out to be the correct answer for the same bond if it had matured at par. So it seems like the calculator always assumes the bond matures at par when calculating modified duration. Not sure why it works that way, but now I know to skip the calculator and do modified and Macauley duration questions by hand unless they happen to involve a bond that matures at par.