MA-118 Lab #4 Name————————————————————————————————————————
Your grandparents are 65 years old and wish to purchase an annuity that will pay them $48,000 per year. (2% interest)
They will receive payments from ages 65 to 85. Excel does not integrate symbolically. You are to
approximate the cost of the annuity by finding the area using LRAM with n =20. Then find the exact
area using the Fundamental theorem of Calculus. In excel to calculate e^x you must use exp(x).
t
base of rectangle
0
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height of the rectangle area of rectangle
1) Do a scatter plot graph of t vs the
height of the rectangle, which would be
the graph of y = 48,000e^(-0.02*t). Print
out a large copy of your graph, then draw
in (by hand) your LRAM rectangles.
2) Find the approximate Area under the
curve using LRAM with n=20? Fill in the
chart at the left and sum up the area of the
those 20 rectangles.
3) Find the approximate cost of
purchasing the annuity, which would be
the approximate area under the curve .
4) How can you make the approximation
better?
5) On a separate piece of paper find the
exact cost of the annuity. Show all work!
Was your approximate cost from (#3)
higher or lower than the actual cost? If
higher why? If lower why?

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