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**Unformatted text preview: **Computing Effective Annual Rates 1 1. Suppose we are told that our investment in a bank will grow at the rate of 8% per annum, compounded quarterly. Say we invest some amount P . What this means is that in 1 year, we will have P 1 + . 08 4 4 = F. F is the future value of our investment. Here, 0.08 is called the quoted rate and . 08 / 4 = 0 . 02 is called the periodic rate . In this example, our investment earns 2% for 4 quarters. More generally, say r is the stated annual interest rate (SAIR), and r is compounded n times a year. Then the following describes how our initial investment of P grows up to be F : P 1 + r n n = F. The periodic rate here is r/n . That’s the rate we earn per period. In general, if we invest for t years, we have P 1 + r n tn = F. We could also use this formula for discounting: P = F 1 + r n- tn . This last formula describes what it is worth for us to have F dollars in t years, compounded n times a year, with an SAIR of r ....

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