# How do I calculate annualised yield from simple interest paid quarterly?

A one-year bank deposit pays 7.25% per annum simple interest, paid quarterly. In other words, it pays 7.25 / 4 = 1.8125% every quarter, for four quarters.

If I were to reinvest this interest, I will earn more interest. How much more? (1 + .018125) ^ 4 - 1. This is assuming that subsequent investments pay the same interest rate, and that they all mature together, one year from the date of the original investment.

But what if the tenure is two years? Am I correct in understanding that the annualised yield remains the same? Therefore, it doesn't matter whether I choose a one-year, two-year or three-year tenure?

• If you re-invest the interest each quarter then the investment is no longer simple interest, but compound interest – DJohnM Apr 2 '16 at 16:07
• I know, which is why the question asks, "How do I calculate annualised yield from simple interest paid quarterly?" In any case, I clarified the question now. – Vaddadi Kartick Apr 3 '16 at 2:42

Your question has a few semantic problems.

Your use of the word simple interest implies that the bank is not paying interest on the interest you receive once a quarter. If that's true the answer's different from the below. But I don't know of any bank that does that, so I'm going to assume you didn't mean to use "simple" as a technical term. If you did, you would need to say at what point does the bank start paying interest on interest? Once a year? Never? Banks don't work that way.

The word annualized means taken to the frequency of one year. An annualized yield is always the yield over the course of a single year. Given a certain total yield over ten years, for example (the "10-year yield"), the annualized yield is the yield that, if you got it each year for 10 years would give you the 10-year yield you have observed. Let R be the 10-year yield. Then the annualized yield is `(1 + R)^(1/10) - 1`.

You have therefore already calculated the annualized yield for your case. It is `(1 + .018125) ^ 4 - 1 = 0.074495`. As written, this is the solution to your question.

You can get the two-year yield, which is `(1 + 0.074495)^2 - 1`, but this number cannot accurately be called annualized.

====== Update after question clarification =======

The annualized return in your scenario is the same whether you use a 1, 2, or 3 year term.

`(1 + .018125) ^ 8 - 1` or more generally `(1 + <interest-per-period>) ^ <nr-of-periods> - 1`