How should I play this? I can't contradict Alara, but this guy seems like the skeptical type that's going to want proof. Hmm…
[Hey, Alto, you're about to be our resident scholar, so play along. If he asks you a math-based question that you're not sure you can answer, then just scratch your nose and I'll tell you the answer.] (Mizuki)
I see Alto nod subtly, and I turn to address the guest.
"I can answer that, Mister…?" (Mizuki)
He turns to me in surprise, but he seems more curious than offended.
"Err…Garvin. I don't believe we've had the pleasure. I manage a couple of banks in the kingdom. I'm eager to hear your answer to this question, Mizuki." (Garvin)
Ahh, that explains the math knowledge. I flipped through the most advanced math book I could find in the palace library – written by one of those Academy guys – and the problems were all trivial by Earth standards.
The most advanced thing was basic compounding interest calculations, and they only involved discreet intervals. Even the author's 'cutting edge' math they mentioned developing was just a method to approximate the slope at a point along simple curved lines. Even basic calculus would blow their minds.
I nod at Garvin politely and gesture towards Alto.
"Alto here is an exceptionally gifted scholar, and I can assure you that her math knowledge is at least as advanced as what's taught at the school you speak of. As you noted, it will be rare that she needs to teach advanced math classes, so other teachers would be employed outside of that subject matter to not infringe on her time too heavily." (Mizuki)
Garvin gives me a puzzled look and turns to Alto.
"Miss Alto, forgive me for being so blunt, but…I know everyone alive who passed such advanced math classes at the Academy. I'm certain you are not one of them." (Garvin)
Alto nods with a neutral expression.
"That's correct. I did attend the Academy, but I was one of the magic scholarship students – I have a power level over 3 and every elemental class affinity. So, I focused on magic and only took basic math classes. Still, as you know, all students have access to the library, and I'm quite fond of reading. If you're skeptical, you could always ask me a question." (Alto)
Atta girl, Alto! Wait…did she really go to this fancy Academy as a scholarship student? Honestly, that would make the most sense given how educated she is as a commoner, and it would explain her studious nature. I'll have to ask her about it later.
Garvin gives Alto…to call it a skeptical look is a huge understatement…but he's skeptical, nonetheless. He pulls out a fold of paper and something that looks like a pencil.
"Very well. Assume you have a product that takes a month to produce in parallel, the product would always be sold for a twenty percent profit, you only have your starting funds and no other streams of income, and all product would be sold immediately after production. What would be the maximum profit on your starting investment after three months?" (Garvin)
Pfffft…it is literally an interest problem. I can do that in my head even with compound interest.
Alto looks a bit nervous, and Garvin extends the paper and pencil towards Alto with a smug expression. Alto scratches her nose.
[Alright Alto, repeat after me. We're going to wipe that smug grin off his face.] (Mizuki)
I start giving Alto instructions by thought message. Alto extends her hand and pushes the folded paper back towards Garvin, and she shakes her head.
"That's simple, I won't need paper. Also, you forgot to mention whether parallel production is completely scalable without a change in the production time or costs, whether production costs must be paid up front and in full, and whether multiple parallel productions can be staggered in sequence, among other things. In the simplest scenario, you could reinvest all profits into each production cycle, and you'd have up to a 72.8% return on investment after three months." (Alto)
Garvin's mouth is hanging open, and Cara is looking at Alto in bewilderment. Zara just looks bored. Alara has gone pale, and she's staring at me, so I give her a quick smirk. Kudra begins laughing hysterically.
"Hehehehe…oh boy, she really got you there, Garvin! You want to take that paper there and check her numbers? I know you can't do it in your head! Fufufufufu…you should let her run your banks, so you'd lose less money!" (Kudra)
Kudra keeps laughing hysterically, and Garvin looks down at the ground embarrassed. His face is a slight shade of red. To his credit, he handles it like a real champ after a few minutes of silence.
"Ehem…Miss Alto, I owe you an apology. You're obviously more than qualified for what Lady Alara described." (Garvin)
Alto gives a polite nod and smile.
"Don't let it trouble you…I accept your apology. I can't take all the credit, either, I had an excellent teacher." (Alto)
[Alto, is that praise for me that I hear? I could get used to this.] (Mizuki)
I see Alto purse her lips. I'd like to think it's done in a grateful way.
At this point, we come to the center of the city, and Eden's massive valley lake can be seen off in the distance to our left. Alara takes the opportunity to redirect conversation and mention that this housing section will have lakefront properties for sale.
"Now, let's make our way to the hot spring. During Eden's early development, it will be the biggest city-owned attraction until the recreation building that I mentioned is finished. It's long, but the walk up the mountain is quite beautiful. Our craftsman is currently working on a magic item that transports people up the mountain more easily. So, if you don't enjoy the walk, it may not be necessary in the future." (Alara)
Alara begins leading the group towards the hot spring stairs, and I feel Cara tighten her arm around mine. I glance over to see her giving me an annoyed look, and she speaks to me softly once I meet her gaze.
"Can I assume that means your Lady will be giving Eden another gift like the train soon?" (Cara)
I grin mischievously at Cara and shrug, then whisper back.
"Perhaps, it's not certain yet." (Mizuki)
Cara seems troubled by my response, and she is silent for a moment. Eventually, she looks back towards me curiously.
"Are you and the rest of Lady Nedonera's party staying here permanently?" (Cara)
"For the foreseeable future, at least." (Mizuki)
"Where? Is it one of those homes I saw to the south when I got off the train? I can't imagine your Lady staying at a basic inn." (Cara)
I smirk over at Cara and shake my head, then subtly turn us so she's facing south, and gesture to the mansion on top of the mountain. She gives me a puzzled expression as I do, but after a few moments of squinting, her eyes go wide in shock, and she turns back to me.
"Mizuki…did you build a mansion on top of a mountain…in a week's time? Also, is Lady Alara really letting you all stay in her new family home?" (Cara)
She is staring at me apprehensively.
"Actually, it's Alto's house, and Lady Alara is staying with us. She did give us permission for it to be there, though." (Mizuki)
Cara seems to grow more pale than usual, and she falls silent. At this point, we make it to the base of the stairs. Suddenly, Cara whispers to me in a shrill voice.
"Mizuki! I can't help but notice that the end of that street in the northern border of the valley has a similar shape as the train station, and it is right near a large opening between the mountains! Is your Lady thinking about building more trains!?" (Cara)
Uh oh, busted. I kind of expected that, though, the layout is obvious. I keep a neutral expression, but nod towards Cara in response. She sighs in exasperation and just looks forward as we begin climbing the mountain stairs to the hot spring.
When we're about halfway up, I feel Cara pressing against me with a tighter grip than before. When I glance at her, I see her looking over the edge of the stairs with a fearful expression.
"I didn't know that you were afraid of heights, Lady Cara." (Mizuki)
I give her a teasing smile, but she snaps her head back towards me and her amber eyes glint dangerously.
"This isn't funny, Mizuki. I've never been on a mountain…most elves haven't." (Cara)
Well…now I feel bad. I sigh deeply and calmly detach our arms from one another. Cara gives me a face of betrayal, but I grab her by the shoulders and quickly swap places with her – now I'm the one closer to the mountain's edge. Then, I loop my arm back through hers.
"Is that better?" (Mizuki)
Cara seems flustered, but grateful.
"Uhm…y-yes, thank you." (Cara)
After that, we continue walking up the mountain, with Alara fielding some of the guests' questions. Eventually, we arrive at the hot spring facilities.
Most of the guests are breathing heavier than normal. However, that's quite impressive compared to Earth humans – we didn't have to stop at all, and nobody is too out of breath to speak. I guess Alara was right about it not being such a big deal.
Looking around, I can see that the hot spring is doing well. The public section of the hot spring is comfortably packed with people, and they all seem to be having a good time.
To my surprise, a fraction of the women are wearing what look like strapless bikini tops, seemingly made from fine leather. It doesn't look like they're in the majority, but that doesn't make it less surprising. Since this world is basically like the dark ages plus magic, I wasn't expecting anything resembling swimsuits.
I was worried about if I should have divided it into gendered spaces with privacy barriers. However, there isn't much of a visitor bias towards men there, and everyone seems to be respecting segregated groups of women and men towards the back. Between that and the swimsuits, I think it's fine.
It looks like all but a couple of the private jacuzzi are occupied. From what I recall, the fee is five copper per person for general entry, and then jacuzzi are three silvers extra. However, the latter hold six people spaciously or up to ten, and the cost can be split, so it's not that bad if you have companions.
"Lady Alara…what are those stone rings with the black domes over them?" (Cara)
"Excellent question, Lady Cara. Those are called jacuzzi, and they let you sit and enjoy the hot spring in privacy!" (Alara)
Cara returns a puzzled expression.
"Doesn't that ruin the point of being at a hot spring? You'd be in the dark with nothing to look at, and unable to feel the open air." (Cara)
Cara seems to be echoing the concerns of other invited guests, and there's a murmur of assent. Alara gives a confident smile and shakes her head.
"Not in this case. The jacuzzi is an enchanted item that only prevents people from seeing into it. If you're sitting inside of it, you wouldn't even know that the black dome is there! You'd see normally and even feel the breeze of the mountain air." (Alara)
There's a round of surprised noises from the guests. I feel Cara's arm tighten around me for a third time, and she slowly turns to glare at me. After a moment, she whispers…
"Let me guess…" (Cara)