forward/premium discounts

One of the practice tests ask for the forward/premium for JPY against USD 12 months from now. According to interest rate parity the JPY would most likely trade at:

the interest rates given are US 7% and Yen 3.88%

My intution would have been to put (1+Rd) / (1+Rf) and get 1.0388/1.07 bc the Yen is the domestic currency here.

The answer says take the interest rate differential 3.88-7 and get -3.12% It then says since Japanese interest rates are lower than US, IRP tells us the forward price of the Yen must be greater than the USD. Hence, it takes more USD to buy JPY forward so the Yen is trading at a premium. Can someone explain why they just subtracted the two interest rates instead of putting the domestic over the foreign and if Forward is equal to the spot times the rf interest rate and the yen had the lower rate wouldn’t its forward rate be lower than the US forward rate???

Someone PLEASE help!

The difference in the interest rates is an approximation to the proper calculation that you described. The correct formula is (1 + 7%) / (1 + 3.88%) - 1. This number is positive (+3.0035%), so the yen is trading at a premium.

How do you know to put the 7% or the US in the numerator?

Dollars increase at the dollar risk-free rate; yen increase at the yen risk-free rate. If we want to know what’s happening to the price of yen, then the yen is the base currency (it’s the commodity, like oil, gold, or pork bellies), and the dollar is the price currency (like the price of oil, the price of gold, or the price of pork bellies).