Answer The annual percentage rate is r ≈ 8.94 % _ The amount after 10 years is A ≈ $ 1833.67 _ Explanation Given information : Initial Investment is $750 &Time to double is 7 3 4 years Concept Involved: Solving for a variable means getting the variable alone in one side of the equation by undoing whatever operation is done to it. Formula Used: For continuous compounding, after t years, the balance A in an account with principal P and annual interest rate r (in decimal form) is given by the formula: A = P e r t Logarithmic property: ln e X = X Calculation: Description Steps Substitute the given information in the formula A = P e r t {P=750, t = 7.75 years} A = 750 e 7.75 r To find the time to double, we need to replace 1500 in place of A 1500 = 750 e 7.75 r Use symmetric property of equality which states that if a = b then b = a to rewrite the equation 750 e 7.75 r = 1500 Divide by 750 on both sides 750 e 7.75 r 750 = 1500 750 Simplify fraction on both sides of the equation e 7.75 r = 2 Take natural logarithm on both sides ln e 7.75 r = ln ( 2 ) Calculation (Continued): Description Steps Apply the logarithmic rule ln e X = X in left side of the equation 7.75 r = ln 2 Divide by 7.75 on both sides 7.75 r 7.75 = ln 2 7.75 Simplify fraction on both sides of the equation r = 0.08944 Rewrite the decimal as percentage r = 0.08944 ⋅ 100 % = 8.94 % Replace 750 for P & 0.0894 for r in the equation A = P e r t A = 750 e 0.0894 t To find the amount after 10 years substitute 10 for t in the equation A = 750 e 0.0894 ( 10 ) = 750 e 0.894 ≈ 1833.67 Conclusion: Initial Investment Annual % Rate Time to Double Amount After 10 years $750 (Given) 8.94 % 7 3 4 years(Given) $1833.67

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 3.5, Problem 9E

To determine

To find : the Annual % Rate and amount after 10 years.

Expert Solution & Answer

Answer to Problem 9E

The annual percentage rate is r≈8.94% _

The amount after 10 years is A≈$1833.67 _

Explanation of Solution

Given information : Initial Investment is $750 &Time to double is 734 years

Concept Involved:

Solving for a variable means getting the variable alone in one side of the equation by undoing whatever operation is done to it.

Formula Used:

For continuous compounding, after t years, the balance A in an account with principal P and annual interest rate r (in decimal form) is given by the formula: A = Pert

Logarithmic property: lneX=X

Calculation:

Description	Steps
Substitute the given information in the formula A = Pert{P=750, t = 7.75 years}	A=750e7.75r
To find the time to double, we need to replace 1500 in place of A	1500=750e7.75r
Use symmetric property of equality which states that if a = b then b = a to rewrite the equation	750e7.75r=1500
Divide by 750 on both sides	750e7.75r750=1500750
Simplify fraction on both sides of the equation	e7.75r=2
Take natural logarithm on both sides	lne7.75r=ln(2)

Calculation (Continued):

Description	Steps
Apply the logarithmic rule lneX=X in left side of the equation	7.75r=ln2
Divide by 7.75 on both sides	7.75r7.75=ln27.75
Simplify fraction on both sides of the equation	r=0.08944
Rewrite the decimal as percentage	r=0.08944⋅100% =8.94%
Replace 750 for P & 0.0894 for r in the equation A = Pert	A =750e0.0894t
To find the amount after 10 years substitute 10 for t in the equation	A=750e0.0894( 10) =750e0.894 ≈1833.67

Conclusion:

Initial Investment	Annual % Rate	Time to Double	Amount After 10 years
$750 (Given)	8.94%	734 years(Given)	$1833.67

Chapter 3.5, Problem 8E

Chapter 3.5, Problem 10E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

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