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How Sinking Funds Relate to Borrowing and Investment Returns

Article Quant Q&A · Author: hyg17
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Summary

The question examines why a sinking fund example might assume that the fund earns a higher rate than the interest charged on a loan. The proposed setup keeps making interest payments to the lender while accumulating money separately to repay principal, which can appear to create an arbitrage opportunity if the higher fund rate were actually available to the borrower.

The brief answer connects the setup to purchasing a productive asset, such as machinery: income generated by the asset and the initial outlay can be modeled as an annuity in a sinking fund problem. This points to a cash flow modeling interpretation rather than a general borrowing and investing strategy. The response gives no detailed derivation or evidence, and it does not explain when a higher fund rate is a realistic assumption; the example should not be treated as proof that risk-free arbitrage is available.

Key ideas

  • A sinking fund accumulates payments intended to repay a loan’s principal.
  • The question distinguishes loan interest payments from saving toward principal repayment.
  • A productive asset’s income may be modeled alongside the initial outlay as an annuity.
  • The short answer offers an illustrative connection but does not establish that a higher investment rate is generally obtainable.

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Fixed incomeRisk managementStatistics
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# Question regarding sinking fund


# Question regarding sinking fund












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.

## Answer by hyg17 (score 0, accepted)

https://quant.stackexchange.com/a/16511

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.