Explanation Given information: The principal is $5000, time is 5 years and table shows the different interest rates. Formula used: Compound interest: Compound interest is calculated by the formula as follows, A ( t ) = P ( 1 + r n ) n t .............(1) Here A ( t ) is the amount after t years, P is principal, r is the interest rate per year, n is the number of times interest in compounded per year and t is the number of years. Calculation: The principal is $5000, rate of interest is 1 % compounded monthly ( n = 12 ) in 5 years. Substitute 5000 for P , 0.01 for r, 12 for n and 5 for t in the equation (1) to obtain the present value A ( t ) as follows, A ( t ) = 5000 ( 1 + 0.01 12 ) 12 ( 5 ) = 5000 ( 1 + 0.00083 ) 60 = 5000 ( 1.00083 ) 12 ≈ 5000 ( 1.05104 ) Further solve the above equation. A ( t ) ≈ 5000 ( 1.05104 ) ≈ 5256.25 Therefore, the value of the investment at 1 % interest rate is $ 5256.25 . Now, calculate the amount with 2 % interest rate as below: Substitute 5000 for P , 0.02 for r, 12 for n and 5 for t in the equation (1) to obtain the present value A ( t ) as follows, A ( t ) = 5000 ( 1 + 0.02 12 ) 12 ( 5 ) = 5000 ( 1 + 0.00167 ) 60 = 5000 ( 1.00167 ) 60 ≈ 5000 ( 1.4928 ) Further solve the above equation. A ( t ) ≈ 5000 ( 1.4928 ) ≈ 5525.39 Therefore, the value of the investment at 2 % interest rate is $ 5525.39 . Calculate the amount with 3 % interest rate as below: Substitute 5000 for P , 0.03 for r, 12 for n and 5 for t in the equation (1) to obtain the present value A ( t ) as follows, A ( t ) = 5000 ( 1 + 0.03 12 ) 12 ( 5 ) = 5000 ( 1 + 0.0025 ) 60 = 5000 ( 1.0025 ) 60 ≈ 5000 ( 1.1616 ) Further solve the above equation. A ( t ) ≈ 5000 ( 1.1616 ) ≈ 5808.08 Therefore, the value of the investment at 3 % interest rate is $ 5808.08 . Again, calculate the amount with 4 % interest rate as below: Substitute 5000 for P , 0

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 4.1, Problem 56E

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The amount at indicated interest rates and also fills the table.

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Chapter 4.1, Problem 55E

Chapter 4.1, Problem 57E

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College Algebra

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The amount at indicated interest rates and also fills the table.

Solution Summary: The author calculates the amount at indicated interest rates and fills a table. The principal is 5000, the rate of interest is 1% compounded monthly.

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To find: The amount at indicated interest rates and also fills the table.

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To find:

The amount at indicated interest rates and also fills the table.