The soil is all wrong. Gravel at the bottom of the pot doesn't improve drainage, and actually makes things worse. The same goes for sand.

Remove the plant from the pot and toss the old soil. Get all the old soil off the roots and let the rootball dry out for a week or two. You want it completely dry. Don't worry, this won't hurt the plant. It stores a lot of water in the trunk.

Next, the soil. There are a couple ways to approach this. Since you're growing indoors, the "gritty mix" is ideal if you can find all the ingredients (see here: http://forums2.gardenweb.com/discussions/2842847/container-soils-water-movement-and-retention-xxii?n=99). If you cannot find those ingredients, mix potting soil with perlite (or pumice, whichever you can find) in a 50/50 ratio.

Finally, planting. The pot you're using looks about the right size. Repot the plant with whatever soil mix you chose. I'd plant a bit higher than you have it in the photo, with the roots just below the soil line. Do not top-dress it with gravel (holds in moisture) and don't water it for another two weeks. Even then, water sparingly until you see new leaves emerging, and in the future don't water until the soil has been completely dry for at least a couple of weeks. Indoors these plants don't use a lot of water. I have one outdoors in a pot here in CA and I water it *maybe* once a month.

Final note on soil. People will come along after me and say you have to use the gritty mix and you should not use soils based on organics under any circumstances. That's not exactly true. The advantage of the gritty mix is that you have less risk of overwatering, which is the biggest danger for people new to container plants. So if you can make the gritty mix, I would do it. If you don't have time or the ingredients aren't available, don't worry, just use the soil/perlite mix, water very infrequently and you should be fine.

Thank you for the detailed response. I have looked, and I don't seem to have access to the items needed to make the grit mix locally. I found this online though, and it seems like a close approximation. What do you think?

https://www.etsy.com/listing/174103811/10-cups-25-quarts-bonsai-soil-60-percent?ref=shop_home_active_4

Does the pot have drainage? The soil you linked is better than anything else you'll find in a store. If possible, use insect screen to sift the small stuff out. I have 2 Ponytail palms, and they both get brown tips on the leaves. Once it warms up, your plant would like to be outside if possible. Acclimate it slowly to full sun.