Can someone explain how we got the theoretical futures price for the following.

5.12. Suppose that the risk-free interest rate is 10% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this create? 5.12 The theoretical futures price is $408.08 which is higher than the actual futures price of $405. Thus, one can construct an arbitrage strategy by taking a long position in a futures contract and a short position in the underlying index. 5.14. The two-month interest rates in Switzerland and the United States are 1% and 2% per annum, respectively, with continuous compounding. The spot price of the Swiss franc is $1.0600. The futures price for a contract deliverable in two months is also $1.0500. What arbitrage opportunities does this create? 5.14 The theoretical futures price is 1.0618 which is higher than the actual futures price of 1.0500. Thus, one should construct arbitrage strategy by selling Swiss Francs and take a long position in the Futures contract to buy back Swiss Francs at maturity. 5.12. Suppose that the risk-free interest rate is 10% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this create? 5.12 The theoretical futures price is $408.08 which is higher than the actual futures price of $405. Thus, one can construct an arbitrage strategy by taking a long position in a futures contract and a short position in the underlying index. 5.14. The two-month interest rates in Switzerland and the United States are 1% and 2% per annum, respectively, with continuous compounding. The spot price of the Swiss franc is $1.0600. The futures price for a contract deliverable in two months is also $1.0500. What arbitrage opportunities does this create? 5.14 The theoretical futures price is 1.0618 which is higher than the actual futures price of 1.0500. Thus, one should construct arbitrage strategy by selling Swiss Francs and take a long position in the Futures contract to buy back Swiss Francs at maturity