Present Value, Discount Rates, and Compounding Conventions

Summary

The document explains how to infer an interest rate from a future cash payment and its present value. In the example, a payment of 400 due in one year has a present value of 320. The accepted answer frames the calculation through the relationship between present value, future value, rate, period length, and compounding frequency. Under annual compounding, the rate is 25%; under continuous compounding, it is about 22.314%. The difference between future and present value divided by the future payment does not give the annual discount rate under the stated convention.

The key caveat is that a rate is not fully specified until the compounding convention is known. The answer also notes simple compounding as a convention that gives 25% for the one-year example. Thus, a present value and payment amount alone can support different quoted rates depending on how interest accrues. The example illustrates the calculation, but does not discuss other conventions, market quoting practices, or additional discounting periods.

Key ideas

• Relate present value to future value using an interest rate and an explicit compounding convention.
• For the one-year example, annual compounding gives a rate of 25%.
• Continuous compounding gives a different rate for the same present and future values.
• State the compounding frequency when reporting an interest or discount rate.

Tags

# Easy interest rate question, but coursera marked it wrong


# Easy interest rate question, but coursera marked it wrong












Here is an easy interest rate question from one of the finance courses on coursera:

> If the present value of \$400 paid one year from now is \$320, what is the one-year interest rate? (Note: this number is also known as the discount rate.)

I took the difference over 400 to get 80/400 = 0.20, but it was counted wrong. I'm wondering if I did something wrong or if the site's answer is wrong. The only other thing I could think of trying is 80/320 = 0.25. Any advice appreciated, thank you.

## Answer by user35980 (score 1)

https://quant.stackexchange.com/a/79138

What you want is to solve $$ 400=320\left(1+\frac{r}{m}\right)^{nm}$$ for $r$. Here $n$ is the interest period (which in your case is 1) and $m$ is the compounding frequency (which you have not defined). For example with annual compounding ($m=1$) or with simple compounding ($m=\frac{1}{n}$), $r$ works out as $0.25$; with continuous compounding ($m=\infty$), $r=0.22314$ ...etc.

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