A. If you were given the equation A = P(1 + r)^t, the interest is compounded annually because there is only one compounding period per year (n = 1).
B. If you were given the equation 1.17, it represents the value of (1 + r) in the formula A = P(1 + r)^t. To find the annual interest rate (r), you would subtract 1 from the given value. In this case, the annual interest rate would be 0.17 or 17%.
C. To represent an account that is compounded monthly, the equation in part B would need to change by adjusting the compounding period. The interest rate (r) would still represent the annual interest, but the exponent (t) would be multiplied by the number of compounding periods per year (n = 12).
D. Using the properties of exponents, the equation from part B, (1 + r)^t, can be rewritten for monthly compounding as (1 + r/12)^(12t). Here, the annual interest rate (r) is divided by 12, and the exponent (t) is multiplied by 12 to account for monthly compounding.
E. To find the approximate monthly interest rate equivalent to the annual interest rate in the equation given in part B, you would need to divide the annual interest rate by 12 (since there are 12 months in a year). For example, if the annual interest rate is 5%, the approximate monthly interest rate would be 5% / 12 = 0.4167% (rounded to four decimal places).
~~~Harsha~~~