银行套利
Bank Arbitrage
题目详情
你有一个债券和一个银行账户，它们的年复利收益率分别为 5% 和 3%。你可以购买债券，也可以借入债券（之后需要归还）。同样地，你也可以向银行借钱（期末归还本金和利息），或者把钱存入银行。这里存在套利机会。如果你总共有 $200，11 年后你能获得多少利润？
You have a bond and bank account that pay 5% and 3% compounded annually. You are allowed to buy or borrow the bond (needing to repay it back later). Similarly, you are able to borrow money from the bank (needing to pay the principal and interest at the end) or deposit money into the bank. There is an arbitrage opportunity. How much profit will you receive at the end of 11 year if you have $200 total?
解析
为了进行套利，你会以较低的银行利率（3%）借钱，然后把资金投资到收益更高的债券（5%）中，并用你手头的 $200 作为抵押；到期后归还贷款本息，保留中间差额。
以 3% 的利率借入 $200、11 年后需要偿还 而将 $200 以 5% 投入债券，11 年后可得到 因此净利润为 这展示了一个无风险收益。
Original Explanation
To make an arbitrage profit, you'll borrow at the lower bank rate (3%) and invest in the higher-yielding bond (5%), using your $200 as collateral, then repay the loan with interest and keep the difference.
With $200 at 3% for 11 years, you owe $200*(1.03)^11 ≈ $276.85, while your $200 invested at 5% earns $200*(1.05)^11 ≈ $342.07, yielding a net profit of $342.07 - $276.85 = at the end of year 11, demonstrating a risk-free gain.