Give typing answer with explanation and conclusion A charity receives donations from a family trust at the rate of f(t) = 12,000 + 400t dollars per year for the next 15 years. If the charity invests the income at an annual rate of 5.3% (compounded continuously), what is the future value of the income? (Round your answer to two decimal places.) What is the present value? (Round your answer to two decimal places.)

​(Nonannual compounding using a calculator​) ​Bowflex's television ads say you can get a fitness machine that sells for $1,020 for $32.01 a month for 36 months. What APR are you paying on this Bowflex​ loan?       The APR you are paying on the loan is nothing​%. ​(Round to two decimal​ places.)

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nt The equation A = P + is used when calculating compound interest from investing P dollars at a rate of r% interest being compounded n times per year for t years. a. Consider an investment ofP = $1000, at a rate of 4% (r = 0.04), being invested for %3D t=25 years. Organize in a table (like shown to the right), the amount A of money n A earned, for each of the following compoundings-per-year: annually (n = 1), semi-annually (n = 2), quarterly (n = 4), monthly, %3D %3D daily, every hour, every second. You don't need to show me any 2 work for this, just make the calculations on a calculator and record the result organized in a table. b. What happens to A as the number of compoundings increase? What did you expect to happen? c. Instead of focusing on investments, consider the function y = (1+±) . Construct a table of values (like in part a) for the same values of n. What does y approach? What did you expect? п d. Use L'Hospital's Rule to evaluate lim (1+ n→∞