IN MAPLE:

We can use the following formula: the future value of a lumpsum A is L := (A, r, n, t) -> A*(1 + r/n)^(n*t);

(you need to execute this command, buy putting the cursor inside this line above and hitting enter. Only then is the formula in the 'working memory' of Maple and you can use it below) --------------------------------------------------------------------

Problem 1: Find the first 20 decimal digits of (a) evalf(sqrt(5), 20); 2.2360679774997896964

(b) exp(1) = 2.718; . . . Problem 2: (a) Plot the functions f(x) = x^3 - 3*x; and g(x) = sin(2*x); in one window. Use gridlines to estimate the solutions to the equation f(x) = g(x);

(b) Find the solutions to f(x) = g(x); exact to five decimals Problem 3: Suppose you deposit $1000 in an account paying an annual rate of 5%. Find the value of the account after 10 years if interest is compounded (a) yearly:

(b) monthly: (c) continuously: Problem 4: If we deposit $1000 in an account earning 8% per year, compounded continuously, plot the time value L(t); over 10 years. Use gridlines, and estimate from the plot when the original deposit has doubled.

Problem 5. What annual interest rate r would allow you to double your initial deposit in 6 years, if interest is compounded (a) yearly

(b) continuously

Problem 6: Find the effective interest rate y if a nominal annual rate r of 12% is compounded a) Quarterly:

b) Continuously:

Problem 7: A well-known rule-of-thumb, known as the "Rule of 72", says that the doubling time (in years) of an account accruing interest, is 72 divided by the interest rate (in percent) - if the rate is compounded annually. How close to accurate is that rule-of thumb?

Answer this question by (a) first looking at the example in problem 4 and 5(a) and comparing the exact answers with the rule-of-thumb answers

(b) by graphing this rule -of-thumb as a function of r, that is, graph the function 72/(100*r), together with the exact formula for doubling time as a function of r, over the domain of r=0% to r=20%.