Question

You will use a graphing calculator to compare savings plans. For instance, suppose you are depositing...

You will use a graphing calculator to compare savings plans. For instance, suppose you are depositing $1000 in a savings account
and are given the following options:
- 6.2% annual interest rate, compounded annually
- 6.1% annual interest rate, compounded quarterly
- 6.0% annual interest rate, compounded continuously

1. For each option, write a function that gives the balance as a function of time t (in years). Graph all three functions in the same viewing window, and within parameters that are applicable for this money problem. Can you find a viewing window that distinguishes among the graphs of the three functions? If so, describe the viewing window by stating xmin, xmax, ymin, and ymax

Homework Answers

Answer #1

Let F(t) = Future value at time t, A = Principal = 1000, r = interest rate, m = No. of times compounded annually, t = No. of years

then F(t) = A(1+(r/m))mt

For option 1:

6.2% annual interest rate compounded annually,

F1(t) = A(1+r)t

F1(t) = 1000*1.062t

For option 2:

6.1% annual interest rate, compounded quarterly,

F2(t) = A(1+r/m)mt

F2(t) = 1000(1+(0.061/4))4t

F2(t) = 1000(1.01525)4t

For option 3:

6% annual interest rate, compounded countinously,

Here the formula changes a little bit,

F3(t) = Aert

F3(t) = 1000e0.06t

Now I have graphed them on an app called Desmos on my phone, use y instead of F(t) and x instead of t

Graph in red describes F1(t), the one in green describes F2(t) and the one in purple describes F3(t)

All three converge to (0,1000) and diverge on both sides afterwards.

You can see that F3 > F1 > F2 in the region t<0

You can see that F2> F1>F3 in the region t>0

You can use the third picture to find

Xmin = 20, Xmax = 24

Ymin = 3624, Ymax = 3632

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