At the end of each year, $6500 is invested in an IRA earning 3% interest compounded annually. Answer parts (A) and (B) below. (A) How much will be in the account at the end of 40 years? Use the following annuity formula, where P= periodic payment, = rate per period, n= number of payments (periods), and F = FV = future value. (1 + i)" - 1 F(P.i,n) = P- There will be $ in the account at the end of 40 years. (Simplify your answer. Do not round until the final answer. Then round to two decimal places as needed.) (B) Use graphical approximation methods to determine the rate of interest that would produce $910,000 in the account at the end of 40 years. An interest rate of approximately % will produce $910,000 in the account at the end of 40 years. (Type an integer or decimal rounded to the nearest tenth as needed.)

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Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
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At the end of each year, $6500 is invested in an IRA earning 3% interest compounded annually. Answer parts (A) and (B) below.
(A) How much will be in the account at the end of 40 years? Use the following annuity formula, where P = periodic payment, i= rate per period, n = number of payments (periods), andF = FV = future value.
(1 + i)" – 1
F(P,i,n) = P
i
There will be $ in the account at the end of 40 years.
(Simplify your answer. Do not round until the final answer. Then round to two decimal places as needed.)
(B) Use graphical approximation methods to determine the rate of interest that would produce $910,000 in the account at the end of 40 years.
An interest rate of approximately % will produce $910,000 in the account at the end of 40 years.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Transcribed Image Text:At the end of each year, $6500 is invested in an IRA earning 3% interest compounded annually. Answer parts (A) and (B) below. (A) How much will be in the account at the end of 40 years? Use the following annuity formula, where P = periodic payment, i= rate per period, n = number of payments (periods), andF = FV = future value. (1 + i)" – 1 F(P,i,n) = P i There will be $ in the account at the end of 40 years. (Simplify your answer. Do not round until the final answer. Then round to two decimal places as needed.) (B) Use graphical approximation methods to determine the rate of interest that would produce $910,000 in the account at the end of 40 years. An interest rate of approximately % will produce $910,000 in the account at the end of 40 years. (Type an integer or decimal rounded to the nearest tenth as needed.)
Let x = f(p,g) be the demand function for tennis rackets and y = g(p,g) be the demand function for tennis balls, where p is the price for 1 unit of
tennis rackets and g is the price for 1 unit of tennis balls. The demand functions for the two products are given such that the demand for either
depends on the price for both. If a decrease in demand for one product results in an increase in demand for another product, the two products are
said to be competitive, or substitute, products. If a decrease in demand for one product results in a decrease in demand for another product,
Test for Competitive and
Complementary Products
Products A
Partial Derivatives
and B
the two products are complementary products. Partial derivatives can be used to test whether two products are competitive, complementary, or
fq(p.q) > 0 and
gp(p.q) > 0
fo(p.q) <0 and
9p(P.q) < 0
fg(p.q) 20 and g, (p.q)<0 Neither
fo(p.q) s0 and g, (p,q) 2 0 Neither
Competitive
(substitute)
neither. Use the test given in the table to the right to determine the relationship between tennis rackets and tennis balls.
x = f(p.q) = 600 – 0.005p2 - 0.002g?
y = g(p.q) = 900 – 0.006p² – 0.004q²
Complementary
.....
Which of the following describes the relationship between tennis rackets and tennis balls?
O A. The two products are complementary.
O B. The two products are competitive.
OC. The two products are neither competitive nor complementary.
Transcribed Image Text:Let x = f(p,g) be the demand function for tennis rackets and y = g(p,g) be the demand function for tennis balls, where p is the price for 1 unit of tennis rackets and g is the price for 1 unit of tennis balls. The demand functions for the two products are given such that the demand for either depends on the price for both. If a decrease in demand for one product results in an increase in demand for another product, the two products are said to be competitive, or substitute, products. If a decrease in demand for one product results in a decrease in demand for another product, Test for Competitive and Complementary Products Products A Partial Derivatives and B the two products are complementary products. Partial derivatives can be used to test whether two products are competitive, complementary, or fq(p.q) > 0 and gp(p.q) > 0 fo(p.q) <0 and 9p(P.q) < 0 fg(p.q) 20 and g, (p.q)<0 Neither fo(p.q) s0 and g, (p,q) 2 0 Neither Competitive (substitute) neither. Use the test given in the table to the right to determine the relationship between tennis rackets and tennis balls. x = f(p.q) = 600 – 0.005p2 - 0.002g? y = g(p.q) = 900 – 0.006p² – 0.004q² Complementary ..... Which of the following describes the relationship between tennis rackets and tennis balls? O A. The two products are complementary. O B. The two products are competitive. OC. The two products are neither competitive nor complementary.
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