MAC1105: Compound Interest and Continuous Exponential Models If $P o is invested at R% interest compounded once per year, the formula is t0 P P (1 r) = + . Interest does not have to be compounded once per year. For example, if the number of annual compound periods increases to 2 , then instead of getting R% interest annually, the interest would be ( R/2)% applied twice a year. So as we divide the interest rate by the number of compound periods, we multiply the number of time intervals by that same number in a slightly adjusted formula. If we denote the number of compound periods as n, the formula becomes nt0 r P P 1 n = + = + . Now suppose we let the number of compound periods increase to ∞ . The formula becomes rt0 P P e = . In these formulas R is called the nominal interest rate. # compound
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