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I am currently studying about financial mathematics for my Exam FM to become an actuary. There is one thing that really bothers me so I would like to have some answers.

Whenever I solve a problem regarding Sinking Fund Method, usually what I see is that the sinking fund has a higher interest rate than the person being charged. And my understanding is that the person keeps paying the interest to the lender, while gathering money on the sinking fund to repay the principal.

Why would anyone do that? If there is a bank that can offer higher interest rate than the interest charged to a loan, then I would simply borrow money, invest the entire thing to the bank and earn money as an arbitrage.

I am probably not seeing how sinking fund works in reality, so I would like to know the reasoning behind this.

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It seems like it is related to a situation where someone can retrieve their principal payment for an object that brings in some income, such as buying a new machine that is highly productive. This income, and initial payment can be considered as an annuity, therefore it can be treated like a sinking fund problem. Although this is just one example, I hope this answers my question a bit.

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